I think the concept of the "House military" needs to be expanded a bit.
There's a feudal system in place throughout most of the Inner Sphere. What you think of as a House military isn't necessarily the same thing as a modern state military. In the US, all the tanks and all the fighter planes belong to the US government. They can distribute them however they want (Army, Navy, Air Force, Marines, National Guard), but basically they own it all. In the Inner Sphere, that's not necessarily the case.
A Fed Suns mech regiment could be the personal property of Hanse Davion. Or it might belong to the government of New Avalon (which is also the property of Hanse Davion). A different regiment might belong to Hanse's third cousin, Grand Duke Doug Davion. All these are considered "House units". They can belong to the Successor Lord himself, or to nobles, or to certain planets, or even to certain interstellar organizations. There might be an ancient mutual defense pact between the members of a state that used to exist 500 years ago, and the Fed Suns still recognizes it and they still maintain some sort of armed forces. Imagine if each US state maintained their own military, and then Texas, Oklahoma, New Mexico, and Arizona had a mutual defense agreement where they maintained an additional level of military.
In other words, there's probably a lot of complexity as far as how the various House militaries are organized that we as players don't see. All these forces are technically subject to the orders of Hanse Davion, but they've also got loyalties elsewhere. We hear mention of units with questionable loyalty, but the game doesn't really go into why. The answer would be that somebody else is actually the one who signs their paychecks.
So when a manufacturer is selling to a "House unit", they aren't always selling direct to the equivalent of the federal government. It's not like Lockheed selling the F-22 to the USA and nobody else. Inner Sphere companies sell to their Successor State, but they're also selling to nobles, individual planets, state-owned corporations, intra-state defense pacts, etc. And now realize that many "mercenary units" are probably like the Kell Hounds, where it's some important noble's cousin's third son who isn't going to inherit squat, but needs a path to glory.
Say that I'm Baron von Backwater, ruler of Backwater V. I maintain a company of mechs as my personal guard (loyal to me, and only me). They protect my holdings on the planet. And then I've got the local Backwater V planetary defense force, which is another company of mechs and a regiment of light vehicles. And then I've got a third company of mechs that are my contribution to House Regiment #217. I don't even see them on my planet, they're off doing whatever General Numbnuts (the House Lord's idiot cousin) wants to do. But I fund them, and as a result the House Lord recognizes my claim to my world. Well I've got three sons. My oldest son is smart and competent, and I plan on leaving control of my world to him. My second son is a complete idiot (probably inbreeding), and I'm pretty sure he's just going to embarrass the family. He'll be a drain on our resources until somebody shoves him out an airlock or he gets shot by a jealous husband. But my third son is competent and ambitious, and I've got to find something for him to do with his life. If I leave him to his own devices, he'll start a civil war on my planet over his inheritance. So what do I do with him?
Well, I could stick him in the House military, send him off to an academy and buy him an officer's commission. But the problem with that is, if he's good, he's going to come back in 20 years as a Colonel or something and he'll want his planet. A better option is that I help him start a mercenary unit. I give him a lance of mechs and a dropship, connect him with another unit that is looking to expand, and I let him seek his fortune. He might get rich, he might get killed. But he'll definitely get sent far away from here.
Anyway, the point of that (long) diatribe is that some mercenary units have every bit of the same access and buying power that a "House" unit does. The latest and greatest designs might show up in a merc unit immediately, if they have the right connections. And a lot of them do have those connections. For those units, I would expect zero delay between introduction of a new mech and when they can start fielding it.