I don't know if it does you much good to allocate a separate FIRE fund and a separate down payment fund.
First, a lot can change in 8 years. The market you're looking at, where it makes more financial sense to buy instead of rent, could flip and become a place where it's more economical to rent. Or you might change and wish to live in different places over time rather than being tied to home ownership. You might realize you're not sure about what you want out of your housing in your to-be-determined post-FIRE lifestyle and decide it's more prudent to try a few different lifestyles over the first 5 years or so.
Second, you have a taxable account that will catch 10k a year of your savings for the next 8 years as long as you stay on your current plan. You can expect that taxable account to become a low six-figure sum in 8 years. Because it can be withdrawn penalty-free, this is your down payment, your Roth backdoor conversion pipeline, or whatever you want. Call it your flexibility money. A house down payment is just one of your options.
Third, you can still estimate a lifestyle cost without locking in a choice on rent vs. buy. One option is to estimate it both ways. Be sure to account for constantly-rising property taxes, maintenance, and insurance on the buying side. Another option is to only estimate the economically sensible housing decision. In many markets, the cost of owning vs. renting are at parity. That is, the amount you spend on housing as an owner comes out to roughly what the rent would have been. These landlords plan to retire when their mortgages are paid off, but have day jobs and barely break even. In other markets, housing prices are prohibitively high, but there are plenty of landlords leveraging real estate - with negative cashflows - just to speculate on further increases. In still other markets, housing prices are so low, there's no point in renting if you plan to stay just a few years. Figure out what your market is and estimate accordingly.
Yes, if you decide you are definitely buying, it makes sense to shift from equity to fixed income investments for a few months.