300 miles from a Tesla 3 is ambitious. You'd need a full battery. IIRC even the long range version tops out at 350 miles (in ideal conditions of course). Tesla recommend that you keep the battery between 20 and 80% whenever possible to increase the battery life, so most of the time the range is much less. Of course, most of the time you don't need 300 miles but it can't be a nice feeling to imagine you're pushing such an expensive component when you do.
I personally would like to check out a Tesla, but I now WFH so the only time I need to drive is usually a dash into York or a road trip 3 or 5 up for a long way. So, I think the Simon's home LPG pump is FAR more interesting!
Maybe worth looking into yourself Miles? Contact a few local-ish gas suppliers, tell them how much you'd expect to use, ask them how much for 47kg bottles delivered to your door, see if you can haggle the price down. Then you just need a pump... You could buy a pump tomorrow from a well known supplier (MIck at LPGAutosupplies, ex TinleyTech) for £600+VAT. If you made the calls on Monday you could be set up ready to refill at home by Tuesday or Wednesday and for a similar cost per litre to refilling at Morrisons.
There's a guy on LPGforum who reckons he uses a £30 car electric petrol pump to pump LPG from bottles into his car LPG tank, I'm not sure if that really works or if it does work how reliable it would be but I've thought about trying the cheap pump myself.
If electric vehicles really do take-off then we could expect forecourts that sell petrol and diesel to decrease in number, we may even see the day when petrol/diesel are difficult to buy and people with petrol/diesel cars have range anxiety. But even then, or even if we couldn't buy petrol or diesel at all, as long as people use LPG for heating and it isn't illegal to run vehicles with engines we would still be able to run our vehicles on LPG if we refuel at home.
With an extra LPG tank fitted my car will do 700 miles on a single fill of LPG. I made my extra tank quick fit / quick remove, I removed it today because I needed the luggage space so at the moment my car only has 350 miles range on LPG. The extra tank is now sat in the yard and it's full. If next week I needed to refuel but all LPG forecourts were out of action I could still put the extra tank in the back, connect it up and drive 350 miles on LPG. In fact I've got loads of tanks in the yard, mostly new ones, any of them could be used as the extra tank and I could carry several of them in my car. I've also got a full 70L forklift tank and a full 18kg propane (caravan) tank - I could easily make a short (3ft) pipe with correct fitting on one end to connect to any of those tanks and quick-fit (hanson coupling) fitting on the other end and run my car from any of those tanks.
Years ago I used to fix local Calor depot's fleet of LPG converted vehicles and got to know a couple of their delivery drivers. The delivery drivers sold me LPG in red bottle forklift tanks, 10 tanks at a time at a price that worked out at around 11p per litre. They'd park on the top road outside my place and we'd simply roll the full bottles downhill 20yards down the driveway into my yard, carry the empty bottles back up to the lorry. I didn't bother trying to pump from the red tanks into my car tank, I just rigged a pipe into the luggage area of my car and carried 2 red forklift bottles in the luggage area. Around 35litres in each of those (small) forklift bottles.