Okay...let's see.
-115% miniaturization is the "standard"; I'll run numbers for 100%, 115%, and 125% (you can treat this as the Yor or a convenient comparison point).
-BHG is the best on tinies whereas BHE is the best on huges. (BHG gives you 17% more firepower than BHE on tinies.)
16 --> 32 --> 34 --> 36
32 (2) --> 80 (5) --> 80 (5) --> 96 (6)
150 --> 300 --> 322 --> 337
250 (10) --> 525 (21) --> 575 (23) --> 600 (24)
96*5=480 vs 600, 1.25 to 1.
I can't even begin to address putting 4 hyperwarp 3s on a tiny. A more accurate comparison with the mechanic I've proposed would be taking up the space of 1 hyperwarp 3, 7 vs 32, while giving you the same speed. I'm not necessarily opposed to 20+ speed ships, even if I don't like them, but that's a discussion for another day.
This would give us 29 spare space on the tinies so I'm going to fake it and say it's 30. We're also slightly under on the huge at 305 when we need 308, so I'm going to pretend that works as well.
This gives me 80 (5) attack tinies and 550 (22) attack huges, which gives me 80x5 for 400 vs 550 or a 1.375x advantage.
But I already said I'd want engines to be larger. A sizemod of 18% is, I feel, far too low.
The problem isn't necessarily that the tinies can't compare in firepower. Nor should they be restricted from comparing in firepower; if anything, they should be somewhat superior in firepower. Why? Because of what the "problem" is: They pop too easily. Once they're gone, they're gone, and the diminished firepower doesn't stand a chance against the huge. Note: I like it that way. That's the way the balance -should- be. But if it's going to work, the smaller hulls need better firepower.
So now that we've addressed what the problem actually is I can concede that you're not actually wrong; you're just wrong about how bad it is and why. Still, the idea that removing the largest advantage will create an even larger advantage is mindboggling at best, even if somewhat true.