unless buying used mecer type trolleys you are unlikely to get away for anything under about R10K if wanting to go lithium. Unless budget is extremely limited I would rather combine an Axpert type 1000W/12V inverter with one of the lithium options. Depending where you shop you might get in very close to R12K.
To power the mentioned loads the flexopower/EcoFlow type jobbies R10-R15K might also work. For me these are not ideal but might do what they want (just look at charging times etc. as this can make these especially troublesome during higher loadshedding stages). While useful these for me are not generally good value.
If wanting to stay Victron + lithium you are unlikely to get it down below R20K.
Don’t know if sold but there is a multiplus 800/12 in the classifieds for R8K. If you add the cheapest 100/200Ah 12V LiFePO4 battery you will be somewhere R16-R18K. Should not need a GX device for this type of setup. Rather spend the extra money on a readyboard on the output of the multi to keep EL protection for the inevitable switchless extension cords all over the place.
If going by your numbers a pylontech and your existing multiplus 1200/48 gets you at R22K odd. Just keep in mind IIRC the pylontech warranty requires cycling and not basic standby use (this might have changed but check). If they think they will be in a position to build up a bigger system at some stage then they at least have a good battery to start with (but also bought into pylontech to some extent).
remember on all options other than flexo/ecoflow there will probably be some fan noise which could also impact overall satisfaction if these things are directly next to the TV.
EDIT: my wall of text doesn’t answer the question of what would I do but variables like budget, circumstances, etc. also need to be included.