I see you fail to mention the most current source, the combat manual availability lists, which have almost none. 3039's upgrades are almost exclusively confined to A rated units with B-rated getting a bit of a boost (as I've contented where virtually all the upgrading would occur the entire thread). That's not 25% of the entire military. It's 25% of <25%. 3052 gives you a bit more reach 1) because it doesn't give you a full list of regiments with their ratings and 2) it has to be playable. IO's tables are basically a prop piece because exactly zero has been done with them, nullifying their usefulness as a source demonstrating anything. Any use of those dates after they were printed is almost entirely speculation at this point, which the kids like to call headcanon.
So it's not ambiguous or conflicting. Until after 3050, HelmTech is pretty darn rare.
I said it depends on the source and it does. You also say that IO's tables are a prop piece. Interstellar Operations is a Core Rule Book. I think that's more than a prop piece. You also say we should go by the lists but those lists are not exhaustive. They're a sampling. Where's the SLDF era Mechs? We know Kurita had some. Where are the Mechs on that mount prototype SLDF technology? I don't see any of the Sorenson's Sabre's mechs listed. Should I go with an incomplete list, or a Core Rule Book?
I also didn't say entire military. I said I didn't think it included militia units or merc units. I also wasn't including Comstar or the Clans. I'd also doubt pirate units were upgraded. That leaves a lot of mechs.
Furthermore, the fact remains that A, B and even C rated units fielded upgraded Mechs. How much of an upgrade varied but Mechs were upgraded. Even Mercenary units received upgrades. At a max rate of 1-2 per lance, that is a sizable portion of mechs. Do I think 50% of all House Mechs were upgraded? No, but that doesn't mean they weren't or couldn't be.
As for playability, are you saying, it isn't possible to play with those tables? I find that hard to believe. I will grant that our list of canon designs is very very limited. I will also grant that customizing designs, without completely outclassing the few canon designs we do have would be a challenge. After all, how many of us wondered about some of the mechs in TRO:3050? I don't that that makes playing impossible though.
I'm fairly certain Sartris is spot on here, and you can infer it a few ways from the lore.
First, the basic smell test for the War of 3039... If the FedCom was able to refit 20-25% of its units with LosTech, prototype or otherwise, giving up the Rasalhague Military District for partial upgrades of 7 Genyosha/Ryuken regiments and 12 Ghost regiments was kind of a raw deal for the Combine. Plus, only the DCMS A* RATs in the Historical: War of 3039 have LosTech, and even then, the force creation rules suggest these only make up 30% of each outfitted A* force (one per lance with a 1/6 chance of 2 per lance). None of the other RATs have LosTech variants/models listed.
There's a lot more units that were upgraded in the DCMS than just the Genyosha/Ryuken and the Ghost Regiments. The rest just have to make do with prototypes. I also wouldn't go by the RATs. They're not complete lists. We also have very very few canon designs using prototype tech. As for raw deals, Kurita got a big buffer zone, and got rid of trouble makers at the same time. They also received regiments worth of mechs. Some with Lostech. Those three things allowed Kurita to survive the War of 3039. I think they're happy about their trade. Also, the FedComs had at least 8 years to upgrade their forces before launching the War of 3039. That's plenty of time to upgrade a lot of their forces.
Second, Interstellar Ops (pp. 102-05) actually has detailed descriptions of just how much of the prototype LosTech was around. Most of the prototypes are worked on and distributed to the most elite of elite units between 3030 and 3040. The (non-prototype) components generally enter production between 3037 and 3040, and we know from the MUL that the first LosTech upgrades (refit kit or new 'Mech) don't start coming online until 3042 or so, with the bulk showing up between 3048 and 3051.
You've just pointed out some of the conflicts and the problems with using lists. The Universal Advancement Table, starting on page 35 lists when items become commonly available. Medium Pulse Lasers became commonly available in 3042. Before then they were available to the DCMS in 3037. In fact the Sorenson's Sabres didn't even test the prototypes until 3048, and the DCMS had them in 3031. Why would the DCMS wait so many years before using them? Especially, when there was a war going on?

As for the MUL, where's all the Mechs with prototype tech? We only have a handful. There should be a lot of variants with prototype tech. Not just one off customs but refit kits and even new production. There should also be variants with recovered tech introduced sooner than the MUL lists.
With that late of a start, it is hard to get more then a few hundred upgraded 'Mechs per successor state by 3050, let alone earlier. The Fed Suns, Lyrans, and Combine each have about 75 to 95 frontline regiments at that time, which comes out to about 8000 to 11,500 'Mechs to upgrade (per state). Even if the major states were able to upgrade 300 Mechs/year for 3048-50 (which might be a stretch), it'd come out to about 8%-11% of frontline units upgraded by the end of 3050. If about a quarter of the 'Mechs in the most favored/elite fifth of forces were upgraded at this time, it would give the remaining regiments a 3%-6% upgrade rate.
What late start? They had years before the Wo39 to upgrade with most prototype tech, and even some production tech.
According to the 20 Year Update sourcebook the Federated Commonwealth alone had a Mech Strength of 268 Regiments, 1 Battalion. With 1 per lance that's between 7,245 and 14,214 being upgraded. Depending on command lances and companies and 3-5 battalions per regiment. That is a lot of mechs but if the Capellan Confederation can recover so well after all their losses in the Succession Wars, the other Houses should find it easy to upgrade their mechs.
Finally, we can work backwards from the deployment tables, equipment ratings, and force description fluff from the Field Manuals. Working backwards from FM:Updates back to the earlier (3059) volumes, we can figure out that any regiment with an "A" or "B" rating (on the A/B/C/D/F scale) is pretty much fully upgraded with mostly new units and even some Clan Tech by 3067. Most of the "A" units are fully upgraded by 3062. We only have the fluff & ratings to go by for the 3059 period, but it suggests that the "A" units are upgraded in the 60%-90% range at this time, while the "B/C" units are about 20%-70% upgraded. There are still quite a few units that have 0% upgrades reported at this time (mostly March Militias and similar low-priority units).
Putting it all together, it suggests an "S-curve" of upgraded tech adoption between the late 3040s and the end of the Civil War era, with very low rates of adoption through 3052, a strong pick up between then and 3062 or so, with close to saturation for the best units and the laggards gradually catching up between then and 3067.
Upgraded from what? Introtech to SLDF or SLDF to new IS tech of the 50s-60s?
I don't see why there would be so little upgrading. Not with so many wars going on. Look at how many mechs the CCAF upgraded with TSM before the 4th Succession War ended? All the Blackjacks with DHSs. And that was 10 years before the War of 3039. Why would the Houses not be upgrading their forces with new tech during that time?