Just addressing some things in random order:
Aside from first bomber sniping too many crucial engineers or maybe a quick 2nd air bomber sniping too many i see no big issues at all with bombers. They're strong yes, but they require micro and create quite some interactive gameplay in the early phases of the game. There is some rng involved with some bombers and the way they drop, but generally against someone who reacts well and prepares a few land scouts to spot raids the bomber can quite easily end up not doing much and you only put yourself behind.
I think a bomber not being able to 1 shot engineers will completely cripple it and make it terrible. Yes, ofcourse you can adjust its stats differently, but this is such a game changing decision that will impact the entire t1 stage balance. If you send a bomber to snipe an expandin engi, you send it to an engi where you have no other units to kill the engi. Leaving the engi on low hp is worthless. You either kill it or it has no impact. Finishing the engi off with a lab or tank basically means you didn't need the bomber regardless. Need 2 passes for the bomber to kill the engi? Basically halves the dps of the bomber and gives the engi an infinitely higher chance of survival because you got tons of extra time to dodge the second pass. This is also the reason why uef/cybran bombers are worse than aeon/sera (if you don't get rng). The engi dodges some of the damage so it doesnt die so you need twice the passes.
drops being 1 shot by bombers shouldn't happen. Don't be greedy and split. Sure they can still brutally rape your drop with multiple passes, but i think that's completely fine. You made the drop while your opponent went for some ints and a bomber to punish it.
bombers being efficient at sniping t1/t2 radars is a no issue imo. I think this is a pretty good interaction. Also literally anything is efficient to snipe these.
first bomber being overly efficient in large teamgames is i think an almost unsolvable issue since it is the same problem (to a smaller degree) as with nukes and smd's. You force all opponents to make the counter. I also don't think any bomber change aside from ruining first bomber bo or not making them 1 shot engineers will fix this, and those changes are terrible for bombers and i don't think they should be implemented.
All in all i think the best way to make early bombers slightly weaker is to slightly decrease their RoF so that you don't snowball succesfull drops at the start when they're being microed.