You’re right about tomatoes getting mushier in a pressure canner. The down side of pressure canning is it takes time to vent the canner, then you count processing time, and then it has to cool enough to safely open it, and then you start all over.
With a hot water bath, the jars are pretty much in and out. You can start the next batch as soon as the previous one is out.
So I don’t think you save time pressure canning something you can hot water bath can. Hot water bath canning is easier. I only pressure can things that CAN’T be hot water bath canned.
I always keep an extra pot of water hot on the stove to add to the canner as the water boils off. That saves time as well.
Do you add and acid like lime or lemon juice to the tomatoes you can using the boiling water bath method?