OK, so first off, any particular reason you'd like/need mesh-capable wifi? Is there no ability to run Cat6 drops to any/all AP locations in the new building? If there's any chance of being able to do do, then opt for APs connected by wire. You get much lower-latency, higher-stability backhaul, and nothing about mesh precludes you from giving up any other differences found in a similarly centralized product (because they're essentially the same otherwise).
Second, apologies if this is completely obvious and/or already taken care of by you and your team, but even the best wifi product will be partially or even completely wasted if proper survey, post-survey engineering and install are left out of the the budget. So, without knowing your status in that area, I would say that perhaps the best return on your $4K could be realized via $2500 of expert labor installing $1500 of budget gear, versus $4K spent purely on premium gear alone. That is not to suggest that you could or couldn't do it correctly yourself(ves), just merely keeping site of the forest for sake of the trees.
As far as specific campus wifi products, if you look at enough integrators, MSPs and corporate in-house teams, you'll basically see three main flavors of gear: 1) SMB/faux-enterprise, 2) firewall vendor and 3) full enterprise. #1 is stuff like Ubiquiti UniFi, MikroTik, Cisco Small Biz, EnGenius, ZyXel, etc., #2 is security-integrated APs from Fortinet, Sophos, WatchGuard, etc. and #3 the top-end stuff like Cisco Aironet, HPE Aruba, Ruckus, AeroHive, Mist.
Each product has its best-fit use-case; it's hard to declare a superior one across the board. Perhaps 15 years ago it would have been easy to just say Aironet, but less so today. Ruckus makes an awfully good case for best physical connection delivery. Aruba probably has the best overall access layer integration. Cisco is usually always class-leading top-to-bottom, but spendy. AeroHive has a great PPSK feature. Mist has pretty cool AI-based optimization and SDN integration capabilities. UniFi's trump card is usually cost savings. So each has its appeal. I would urge, though, that perhaps brands/models be put in hindsight if what I suggested above seemed to strike any nerves. The engineering and install will play as much, if not more, of a role in the overall outcome as gear itself.
Hope some of that helped!
