FWIW It cost me $800 for both felt liner and the rubber liner 15 years ago. It was I think 40ftx30ft and I cut it down to size once I laid in the hole.
Search for pond liner suppliers on-line. PondBoss may have some great suppliers for this as well, though I don't know who is a supporter.
Anything over 20x20 is frigging heavy and awkward. You will need friends to help or a small tractor with a fork. I had a teenager slave labor.

Process is as follows:
1. Measure size, calculate depth and liner sizes needed. Order parts. (Measure what you have already)
2. Rent a machine for rough hole digging. The vast majority of material is removed this way. Use a small trash pump to keep water out when working. Or use existing hole, though you need to remove that island.
3. Dig hole with rough features with rented machine (maybe a few hours more to remove island). In your case maybe you will need to dig a drain out to a road ditch from the hole as well. Maybe a powered small dump to move soil elsewhere, or you can pile the soil as part of the pond feature on one side for plantings or future waterfall. Don't make too tall, spread wide and low or it will look like a mini volcano. (I was lucky and a neighbor had a machine and worked it for free, and I used a manual wheelbarrow to move soil, it was hard)
4. Use a laser-level and hand shovel to pull material from the basin and create a at least 1ft wide level rim around the perimeter. Use wood stakes with the level line marked to fill to. I set mine about 2" above surrounding lawn level to drape liner across as weed barrier. This is a lot of manual effort. Great way to get in shape. I'm too cheap to pay someone else to dig.
5. Manually create tiers/steps/bottom features to hold plants and allow yourself easy access to the basin. The stairs should angle towards the sides a bit so you don't fall in easily. Expect to slip in anyways when working on it, so always wear bathing suit once full. This process isn't too bad, but is manual work. For the most part it is just arranging soil in the basin to make the features. The key feature is a step starting at about 1ft under the water line that will support stones/cobbles from that point up and over the rim of the liner once the liner is in. A bonus would be to add a rim on the edge to prevent things from easily sliding down. A thick rope staked down would do the trick, or 0.5x1 treated lumber set down a little. You don't want to need stone all the way to the bottom. That can use pea gravel or leave bare or just a few larger rocks here and there. You can use landscape blocks for stairs, just be careful of sharp edges. Double up in the felt on those features if concerned.
6. Remove all roots and check for any sharp edges. Lay down the felt. It comes in easy to manage sizes.
7. Pull liner across with friends. Tamp down, re-adjust some features, push into corners, make folds as needed. Easy. Maybe an hour or two.
8. Cut liner to the outside of the rim you made, It should still go up and over and that's it.
9. Use baseball and larger size cobbles and start building up from the shelf. I interspersed with large rocks, 2ft diameter stuff for a natural look. Some I left isolated out in the water. I have plenty of rocks on my property to work with, but did need more rocks from a local gravel pit for more interesting stone. When all placed, use pea gravel and sand in the gaps. This sort of locks things in place.
10. Fill.
11. Buy some plants, get them in there where you would like.
12. Wait about a month before introducing fish. Rubber liner ponds take longer to settle the nitrogen cycle than soil-based. Goldfish can take it, but not much else.

Your largest problem may be the liner trying to float up from the high water table. Using a variety of stone and gravel to pin it down will be important. The drainage ditch for the groundwater to help with your wet spot could double as a source for water if your well isn't up to snuff.

Using your own labor, you can probably get the cost well under $3K total including ordering stone, pipe for drainage, and renting equipment.
Don't go deeper than 5ft, any deeper and it is hard to maintain. Use a simple air line to an indoor diaphragm air pump at the house. It is all you need to turn the water over and prevent complete ice-lockup in the winter.

That price you got quoted is OBSCENE. A flat out joke. Who would spend that much on a project that is rewarding, easy, and for the most part can do yourself unless you have health issues?