Susan - you should always follow your legal advice although worth confirming what needs to be done with a conveyancing solicitor as well.
I don't quite follow what it is you are now asking although it reads like you want to sell your own property before you then deal with the deceased's property and move in there.
If you are applying to HMLR for the register to be updated in anyway and there is then an urgency involved you can submit the application first and then
request expedition
Expedition can reduce the wait time from a few months to a couple of weeks but everything then needs to be in order of course to enable the register to be updated as applied for.
You don;t have to wait for a purchase to be registered before 'moving in'. Many purchasers complete and move in. The register update then happens later