Anybody have any suggestions on how to go about making a trip to Tikal for overnight and about what this would cost? Thanks

I will just answer on accomodations.
You can stay overnight in Flores which is in the middle of a rising lake with an always flooding road to it on a causeway. Rooms from US$10 to US$100.Some modest priced rooms we saw on the second floor in a hotel whose lobby is underwater. A dugout canoe takes you across the street.
Tikal is a short bus ride away. I think the best way is to stay at an expensive US$60 to US$100 room at the ruins entrance. There are several hotels and they often book full. If you do this you can ask the rangers in the park to validate your ticket for a reentry at night for no charge.This is a Tikal you won't forget. The place seems less ruined at night. Howler monkeys and a moon rise to remember. Ancient vibes.
The next morning you may find the hotel grounds full of monkeys ,peacocks, every kind of wildlife that the staff has befriended. We played with a baby ocelot all morning one day.
The staff of Tikal Inn told us a story about a margay that some Guat tourists took in their car to steal and take home for a pet. The police rescued the Guatamalan couple a few miles up the road in a ditch. Hint: don't try to hold a wild cat on your lap if he wants to leave.

The fastest, easiest, and most comfortable way is to fly. Of course it is also the most expensive. Tropic Air has a package on their website.

Maya-Island Air also does the Tikal trip.

One way fare is: $88.00 US per person; departure tax at the airport is: $20.00 US

Day Trip and Overnight Trips can also be arranged.

Check Out: www.staycayecaulker.com/trips.html

for the rates on Day Trips and Overnight Packages (including hotel).

There is also a bus from the water taxi terminal in Belize City. A really nice bus. I don't know the price but it once was US$19 each way.