To remove the original (factory) bitumen coating on the floor panels inside the car, I used an old wood chisel and mallet (I was hardly going to use a new chisel, was I? and note I
did use a mallet, not a hammer - I'm not a heathen!), this took a long time but was controllable
and I didn't sustain any injuries.
Some people recommend using a hot-air gun to soften the coating and then remove as much as possible using a decorator's scraper. Some say that using 'dry ice' will make the coating brittle allowing it to be shattered by a hammer blow. Others might recommend using an air chisel or maybe an air-operated needle de-scaler but these will likely punch holes in any weakened metal, plus you may injure yourself... Experts will say sand or soda blasting is the only way but I realise you're working at home (strange that these experts are the one's offering this service for a fee....).
I'm always in favour of minimal cutting out when repairing rust damage (have gotten myself into mucho trouble by cutting out large chunks

) and tend to tackle one relatively small area at a time. Remember that and depressions/hollows pressed into the floor pan are there for a reason e.g. to allow big feet to operate the pedals (Jaguar made this mistake on the early, so-called 'flat-floor' XKE types and had to incorporate a step down for this reason - strange that collectors will pay a lot more for these very early cars, I hope they've got smalll feet). Also, if you omit these depressions, the original carpet may not fit so well.
If you do however decide to buy and fit replacement floor pans, check if they are high enough at the sides to attach to sound metal - the rust often extends above any original perimeter turn-up/attachment, so you might have to make up repair sections to install at the sides before fitting the new floor pans.
Afaik, floor pans are usually installed from above - under the floor pans are various pressed steel strengthening members which will need to be retained or remade if they don't come with the new floor pans, plus consideration has to be given to the seat rail mountings etc.
Before cutting away any metal, it's a good idea to support the sill/rocker-panel ? to prevent any sag being introduced as you cut away metal. The sills/rocker panels are critical on a Spider and need to be in very sound condition (afaik, there is a centre diaphragm? panel inside between the inner and outer rocker panels, these can rust away unseen). Some people temporarily weld a support bar across the door opening to maintain correct alignment but I prefer a support under the sill/rocker + careful measurements of the door opening having been taken before any cutting and double-checked again before any welding is carried out.