You are absolutely correct, I spaced it and did not stick the landing on my breakdown at all--which is why nobody pays me for this.
So, continuing the back of the envelope math, we can speculate as to the hit we'll take on additional draft picks using the estimates put out by overthecap.com. Assuming dealing Rodgers now and keeping all our current draft picks puts us more or less at the salary cap, every pick added puts us over the cap and would require a subsequent cut that at least matches their cap number.
The Jets' 1st round pick (#13) is projected to have a cap hit of $3.4m in 2023. Their 2nd round pick (#43): $1.6m. 3rd round (#74): $1m.
Just for fun, here's the cap hits for each of the top three picks for some other possible landing spots:
Raiders: (#7) $4.8m, (#38) $1.7m, (#70) $1m
Dolphins: (no 1st, punished for the Brady tampering fiasco), (#51) $1.3m, (#77) $1m
Panthers: (#9) $4.2m, (#39) $1.7m, (#61) $1.1m
Titans: (#11) $3.8m, (#41) $1.6m, (#72) $1m
Colts: (#4) $6.6m, (#35) $1.8m, (#79) $1m
So, all in all, trading him now seems pretty financially viable. The complicating factor would be if the buying team starts to get cute and expect Gutey and Ball to pick up some of Rodgers' salary, or if Rodgers balks at restructuring his deal for the buying team, which would (presumably) lower our draft pick haul considerably.