I'd rent a power snake, access the main drain from the basement clean-out, and extend it from there to the sewer connection.
By using the right size snake and cutter head and running it in and out slowly multiple times, you should end up with a much better flowing drain. Having a tub faucet on, and the tub drain unplugged, while doing this should provide enough flow to rinse the debris to the sewer. (If you have a septic tank, it will go there and wait for the tank to be pumped out.)

Call your local drain cleaning companies and see if any of them do hydroblasting.

They run a high pressure hose in the drain that has a special head to pressure wash the line. It is the most effective way to get caked buildup gunk off out of the line.

You should also be aware that buildups are often at a 'belly' in the line (a dip) where it does not drain completely.

The solids settle out and can eventually harden to block the line.

Even if you clear the line, if it has a belly the problem will return