You should study the rental contract. It might contain a clause that the tank has to be brought back which would cause a lot of trouble/costs. Most tank companies would offer this service but charge you for it: emptying it, disconnecting it, lifting it over the house with a crane might be necessary because the access could be blocked since the original placing.
So the second thing you should think about is how to bring in a new, bought tank. If that is possible then the company delivering the new tank should be able as well to pick up the old tank and transport it to the owner company.
The third job is the dealing: get an offer for the entire job and confront the tank rental company with the alternative to sell you the tank they are already renting to you.
You have to be tough in this dealing, maybe the rental company will lower their price for LPG delivered to you to stay in the lucrative business of renting. If they are showing good will get it fixed in a contract, a reduction for a short period won’t do, you would be in the same position as before after a short time. A good sample for an agreement would be a clause that they would deliver for a similar price as the best offer on the market from a free/independant trader. But still you would be stuck with the rental costs, which could be raised by them as well. And a tank in ownership is a better sales argument for the house than a tank rented to (may be) changing conditions and general high prices for the LPG itself.
Good luck, and let us know how it goes.