A nice thought experiment. Assuming the property has no significant sentimental value and you don't have to make the decision immediately - I'd spend some time researching, and if I couldn't find any indication of it being worth more than $2 mils, I'd sell it, buy a similar one and enjoy the difference.
Here's the thing. It's much easier to do the research on something that's been on the market for hundreds of years. Our grandparents used to trade land, but not many people have traded bitcoin and know what the real value behind it is. I'm willing to bet it would take you a lot of time to find if it is or isn't worth the price they're offering. It's good that you're giving it a deeper thought though.
This is not at all similar to the first part of your post though. If they offer to pay you above the market price, just sell it to them and buy back cheaper immediately. No dilemma here.
They aren't going to offer you more than the market price, but the market price will become unstable due to high demand. Imagine that one day it's worth 50k, the next day 51k, the next 55k, after a month it's 100k. You know the institutions are pumping it, you know the demand is high. They're already offering you 100% above what the market price was a month ago, but you wait another month and they're again offering 100% above that. What's the real value then? The price from January, February, March? Maybe the real price is what they'll be offering in a week, or in a month?
I hope you understand where I'm trying to go here. They'll not say that they'll give you 100k when the market price is 50k, but they will pump the price for you to feel the incentive to sell. I believe there will come a day when if you choose any single day in a year to sell your bitcoin it will be below value, meaning that if you do it on 10th of May, on 10th of June it will be 20% higher and so on.
The question is what you do when faced with constant demand? Do you dump it thinking it can't get any better, or do you hold thinking they must know something you don't since there was no such event in the history of bitcoin, so there's no historical data for you to rely on.