If it's feasible, we might want to consider implementing the following (or some approximation thereof):
Once 7:00 P.M. has arrived, if we're not already "upstairs" (3rd Floor Banquet Facility: "The China Room"), promptly move upstairs. "Immediately" collect dinner fees, and pass that to the wait staff.
Issue dinner "tickets" or coupons (or some type of token) as folks pay their fees - this will help make easier tracking who has and/or hasn't paid (both to wait staff and any among us collecting the fees and running them to the wait staff).
Also, as soon as the first funds (very shortly after 7:00 P.M.) are delivered to wait staff, the general direction to the wait staff should be to start working on bringing food, and that's what we have so far, but that we may have more in short order.
Station a "volunteer" from 7:00 P.M. to 7:10 P.M. by the doorway of the 3rd Floor Banquet Facility: "The China Room", as stragglers come in during that time frame, collect dinner fees and issue "tickets", and as practical/feasible, make runs down to or pass the additional fees to the wait staff as soon as practicable.
Also, "tickets" - if we used a roll of the 2-part type tickets, we could also use the other part of it for raffle drawings (e.g. door prizes - could just put out a hat or bag, anyone that wanted to enter could drop the "coupon" part of their ticket in there, and drawing could be done later from those).
Once 7:10 P.M. has arrived, the "volunteer" door monitor should run any remaining fees for dinner not already delivered to the wait staff, to the wait staff, and then the "volunteer" can of course join and be seated with us (they may want to reserve their chair with jacket or such ahead of time, so then get a good seat selection).
7:10 P.M. is our official cutoff (though we don't and probably wouldn't rigorously enforce that). Any stragglers that come in after that (depending on how late, available seating, whether they actually want to eat dinner, wait staff ability to also accommodate them, etc.) we could collect fee and deliver it to wait staff - or they might miss out on dinner.
Rationale/theory: This would encourage folks to be there in a bit more timely manner (e.g. less waiting time between 7:00 P.M. and first food delivery), hence folks would become more motivated to make it there by 7:00 P.M. Food would arrive earlier (probably as early as ~7:10 to ~7:15 P.M., instead of our current typical 7:20 to 7:30 P.M.). When we have speakers/presentation, etc., that allows more time for that. Meetings may also wind down slightly earlier, affording folks more convenient opportunity to make it out of there and home that much sooner.
Other random idea: try to have folks seated at tables with 5 or 6 people per table at least "initially" (when and around the time most folks arrive). This would allow us to better accommodate stragglers (if I'm not mistaken, I think tables comfortably accommodate 8, and squeeze up to 10 or maybe a very crowded 11, but 8 is a much more comfortable fit).