Game 1 - after ... Qg6, 7. Be3 then W is better developed and the threats include Nh4, Nd5, xc7 creating some difficulty in a queenside cackle 0-0-0. Sample line 7 Be3 Bd7 8 Nh4 Qf6 9 Nd5 Qd8 (if ..xh4 then Nxc7) 10 Qh5+ with a +4.25 evaluation. The Budapest makes for fighting chess!
Game 2 - White (you) had a gorgeous position with a P up and good squares for your pieces. However the QS majority is backward and Black has nice dark squares for his N's also (since W's dark sq B is eternally gone). The W Bishop is inert but White's squares on e6 and c6 are painful for Black, especially if the N's can be coordinated with any major officers. One suggestion for W getting that R-N-Q coordination would be to double or triple R's and/or Q on the e-file and try to penetrate on e7, with or without a KS pawn storm. ... point is you had an outstanding or winning game at that point. A shame the rook drop had to ruin an exciting battle.
Next time you open with 1.d4 I'll be playing some other system! This is twice now you've effortlessly achieved a plus against my fave system!
Game 3 - Agree with your analysis totally. Had the R gone back to ...Rg4 and you followed with ...h4 I'd have needed to exchange Q's and pronto.
....
Mojician understands chess profoundly, as an 1800+ player at least; it's only his occasional tactical oversights that hold him back from such a rating. This happens often; very high-IQ chessplayers are very strong in strategy but subject to missing the finer details of tactical combos. A malady Dr. D fights himself...
Looking forward to next battles! :- )
Warmly,
Jeff