As I understand it, from the moment a peerage is accepted, you cannot enter the House of Commons. There is nothing in place to facilitate a delay in acceptance as all nominees are put to the King for a letters patent seal. If an mp wants to continue in the HoC even for a short time, they have to decline the title. Maybe Liz will ask the King to change the protocol regarding the letters patent seal? By agreeing to it, the King may be accused of " meddling" in politics though.
The only other way round it, would be for Truss to make them all ministers, as Lords are allowed to act as ministers for the government. As usual, with this government, it's a very grey area, as no Prime Minister has tried to avoid a by election of a departing MP before.