There should be a section where you configure the DHCP settings (the range, etc) and in there is a place for the DNS you want to use on the LAN. Then again, maybe it always enforces using itself, and the only place you can edit anything is the UDM's upstream server, which is what you've already done. As mentioned that does work with Pi-hole but it means all your client lookups appear to come from the UDM, and that means you can't easily separate stuff out and leads to rate limit issues.
You may be able to sidestep the rate-limit issues if you change the thresholds in Settings > DNS > Rate-limiting and increase the numbers a bit. That won't help with splitting up the queries though.
Hopefully there is a place for the DHCP DNS setting buried in the UDM somewhere and you can edit it. Have a good scout around. If you do find a place where it's located by all means post a followup and a screenshot, that will help any future visitor with the same model.
If the UDM really is crippled like this, then another option is to disable its DHCP entirely and switch on the DHCP server in the Pi-hole (in Settings > DHCP) instead. That will allow the Pi-hole to take over the role. The Pi-hole DHCP uses itself for DNS as default.
You would have to set the DHCP IP range needed. Once it was ready you'd have to take everything off the network and back on so they all pick up their new IP addresses from the Pi-hole's DHCP.
Using this approach gives you back control, lets you see individual devices in Pi-hole, and turns your UDM into basically just connectivity and a gateway for the traffic in and out. Here's a post about it on this forum.