Absolutely. Cut all those extra shoots and branches down to the trunk and then paint it with Bonide Pruning Sealer or equivalent, then wrap it with an opaque tree wrap, not burlap, something with wound protection in mind.

Then you want to fuse the centermost shoots/branches by lashing them together; I like anodized aluminum wire (bonsai wire) for this because it’s easy to work with and allows a little stretch, you can use zip ties as well.

Here’s an article that touches on the technique. See the part about thickening branches. Basically, you’re going to grow the branches so close to each other that in a few seasons they are just one branch.

Bonsai training is the ticket here, for your research. Plenty of people do bonsai hydrangea and someone have probably written about fusion techniques specific to hydrangea.

Depending on where you are, after that massive prune, it might not be the right season to cut it back much further. You might want to cut all the branches outside of the center back by several more inches, so that they are all shorter then the center branches, and then do the remaining cutting and begin the fuse in winter.

Ymmv.

https://www.bonsaihunk.us/public_html/?tag=fusion

There’s also the opposite technique of trunk fusion, which is trunk splitting. You may find that once you get in there, there are several different plants that want to come apart. You can break them on their seams if’n you find seams, and then done proper trunk merge.

https://www.bonsaiempire.com/blog/trunk-fusion

I think it would be too much effort to try and train an old shrub into a tree when hydrangeas are so insanely easy to take cuttings of, and the cuttings grow so fast. (So much so that when we prune our hydrangeas many of the fallen branches accidentally become new plants).

tho I love hydrangea bush’s too and this is a lovely mature one. So I reackon you should keep this one, take a cutting, and grow the cutting into a tree somewhere else, and then you get the best of both worlds (:

If it’s dying back to the ground every year, training it into a tree might not be the best idea.