C3 is one option, albeit an expensive one, as it adds 30% to the BV2 of each mech in the network. Targeting computers also help.
Also, though, you made a classic mistake in the tonnage areas --- and that is, you were systematically lighter than your opponent, for dubious returns ..... Lighter machines have to be focused on their role, as they don't have the tonnage to play jack of all trades. Second, your armor is always going to be lighter .... so you cannot slug it out.
In addition, the ERPPC is not the hole puncher it used to be..... you can use it, but you have to consider it in all of it's benefits and limitations --- it's hot, and only gives you a 10 point hit. In 3025 tech, 10 points was great... in later eras, it's pretty average.
If the terrain is open enough that he could get runs of 8, to counter your jump 6, then you were in the wrong terrain already.
I tend to favor both lighter units, and longer ranges.... and letting yourself get cornered on 4 map sheets tells me that either you really had some bad initiative rolls, or you focused too hard on trying to control range, and let yourself get cornered. Knowing when to keep the range open, and when to do a quick runby to re-open range, is a skillset that takes time to develop.... and practice is the only way to do it.
Second while you did have some decent stuff there, there was nothing that was particularly exceptional. When you use a light fast striker force, especially geared for long range, things like jump jets are an option.... because they cost --- as in, when you have jump jets, you are also paying for the opportunity to do death from above... even if you never try it. And in any terrain where your opponent is close to your speed, where running gives him more options than your jump, you are in a rough spot.
For the type of terrain you are describing, a mech like the Talon probably would have served you better.
http://www.sarna.net/wiki/Talon_%28BattleMech%29Lastly, I am looking at his force, and trying to figure out how much ammo he was carrying for that AC/20
Precision ammo is half shots per tonnage, rounded down, so a ton of precision ammo is only 2 shots on the AC/20 per ton. So it is possible to run him out of ammo, but probably only with units that have the armor, just in case. And also, remember that precision ammo is NOT a base +2 bonus, but instead negates up to +2 of the targets movement mod -- that means that at long range, if you force them to run to get there, and with basic gunnery, they would need a 10+ to hit you. If you can generate a +3 or better, then you add to that number, and make it even harder. However, a heavily armored slower unit can actually be the bane of precision ammo, especially on an AC/20, because the ranges are so restricted, just move enough to control range, but never give your opponent the advantage he is going for.
As for options you could have used --- when going for long range, open areas are your friends --- you want to use range to keep your opponent from firing, not terrain.
Second, smoke is your friend --- even the lowly LRM5, or SRM2, can produce smoke that can be used to block LOS, and make it far more difficult for your opponents to shoot at you.
Finally, accept that you might get into a position where you either have to close to get by an opponent, or just to finish things, so weapons like SRM's, and especially, the Snub nosed PPC, can be very useful for that.
In the end, though with the mechs you listed, you traded speed for the flexibility of jumps, and on more open maps, that is not always the best choice.
Nahuris