No one can judge from pictures if the BOM is loaded identically for both boards. Although the amplifier front-end IC can do 800MHz, the bandwidth limit options could also be set externally. E.g. both the HDO1k and HDO4k have 3 tiers of bandwidth: perhaps this is the max amount of bandwidth limit taps the front-end can support (besides 20MHz) by switching in a few extra passives externally. Many 0402 passives and/or capacitors don't have markings, so it's not possible to tell from pictures if they are different.
W.r.t. FPGA bitstreams: modifying them is not so easy. Many FPGA bitstream formats are not even open format, so good luck finding the right bits for modification. Moreover FPGA vendors/customers are very concerned about protecting IP.. and since most FPGAs are volatile devices (and thus the firmware is loaded externally on-boot), the loaded bitstream must also be protected outside the device. Newer FPGAs support encrypted bitstreams which can't (easily) be modified. With a bit of bad luck, Rigol has decided to use different AES decrypt keys for HDO1k/HDO4k, so transplanting FPGA just the images won't work. Most likely this key is set to read-only on the eFUSE of the FPGA.
Then there the part that a HDO4k FPGA bitstream can very well assume 2 ADCs are fitted. So even if you jumped through all these obstacles to get an image to run.. the device may very will malfunction at this stage without a 2nd ADC fitted. I agree with
@2N3055, these are a lot of assumptions and transplanting ADCs is a very risky move to potentially brick 2 scopes. But one can only dream and hope. A hack from 70MHz to 200MHz is still quite decent, as that's a bandwidth jump lots of people were happy with for the Rigol 2000 series.
I'm not sure if Rigol is willing to protect their sales of the HDO4k that little. Purely from starting price and max BW, you can tell the HDO4k and HDO1k have different target groups. The HDO1k is still within hobbyist budget reach. We have one HDO4k on order at work because we don't want to fuss around with hacks and other potentially accuracy/reliability-affecting modifications.