Contractors run from 203 projects to begin with. With an unrealistic budget, the only folks you’ll have interested will work outside the 203, and be hacks using cheepchinesecrapola.

Save your money. Have it make some friends. Like 3x friends. Then approach the project again when you have the funds to tackle it properly and with some thought by a good Kitchen Designer.

Thanks Sophie - that's kind of what I've been thinking. I don't want to rush it and I think that I'd like to contemplate the design for a while, do some ourselves, find salvage pieces to incorporate so the remodel is true to the 1915 home, etc.

That sounds like a better plan. After all, the kitchen is in good shape and is clean, so it is a pleasant place to work. If you can get period-correct cabinetry, you will be way ahead compared to the Ikea you will be able to afford with $20k.