Blocking Bathtub Overflow Valve?

I just moved into an apartment with a claw foot tub. The tub is located below a set of stairs so there is not shower capabilities. There is a hand held nozzle that I can use but I'm getting comfortable with the idea of taking baths daily.

Here is my problem that I am searching for suggestions. The main drain has a stopper that works excellently. There is a separate drain about 5 inches below the faucet that if the water gets to that point will automatically drain it out.

I won't lie, I'm not a size 0 person, so I need more water to cover my body than a smaller person might. When I fill it to a point (with me in it), where it covers my body it takes about 10 seconds before the waters drains out super fast and then I'm back to square one.

How can I keep the second drain from draining automatically, both so I can soak in the water but also so I don't have to hear that loud gurgling sound while I'm trying to relax? Any and all suggestions are much appreciated!

Danielle from Hoboken, NJ