re: HVAC for basement

Sounds like the guy who says 18,000 BTUs is to large might be correct as basements don’t have much heat load (no roof, minimal air filtration, etc.) but here’s a free on-line manual J calculator for estimating heat load and sizing of the HVAC (manual S) LINK if you want to try to estimate it yourself. If a HVAC is not running, it’s not dehumidifying.

I can’t tell you if the single 9000 BTU guys approach for distributing air among 2 rooms is appropriate, but did no contractor mention a single mini-split with 2 heads option - 1 per room?

Also since humidity is often the major comfort issue in basements, have you thought of coupling the HVAC with a dehumidifier which control humidity when the HVAC is not operating?