Waiting eagerly for better swimmers to respond, but just observing that planks and burpees rely on core flexion strength, like a crunch, and holding your legs up in the water in theory relies on core extension strength.

Lay on your stomach in a Superman pose. Raise your feet and arms slightly and hold that position. Start with short holds and then lengthen the time as you get stronger.

Prone plank.
2 leg bridge with band.
1 leg bridge with band,
Side plank
Bird dog with band
Paloff press, weight as tolerated or with band.
Clamshell. With band.

I’ve been doing these every day for 10 weeks for rehabbing after surgery.
100m time went from 1:34 to 1:28 SCM.

PT is a way of life, not a patch.

I like doing stability ball hamstring curls and static stability ball bridges (holding the starting position of the curl for 45-60s).


https://www.youtube.com/watch?v=GKMD68CZfFM



Also, swiss ball russian twists. These would add a nice torsional/rotational element while still engaging the key muscles you're trying to target.


https://www.youtube.com/watch?v=SxAUxHQlv20

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I am not a master swimmer by any means, but I second this. I would also add that when you build up the ability to hold for a decent amount, that you also include doing it as a dynamic movement...meaning go from arms spread and legs spread on the ground to off the ground and up in the air (like you are flying) to back down...repeat like it's a set.

Once you do that well, combine the two. Hold the superman pose, go right into a set as I described above, and back to the superman pose. Burns like a mother, but helps.

I need to get back to it myself.

This. I'll add that it really takes very little strength to keep your legs up while swimming; the water does most of the work. It's more a matter of imprinting that position so your legs sort of stay there by themselves.

One important thing is to make sure your hip flexors (and quads to a lesser extent) are loose enough that you can maintain this position without fighting inflexibility. Runners and cyclists tend to have tight hip flexors, which means they have to use more strength to overcome that tightness.

There have been a number of threads including this video that have many testimonials to success that people have had.

(edit)

When doing the Superman pose, feel what muscles you are using to lift your legs (back, butt, hamstrings). Then focus on using those muscles in the water.

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"Go yell at an M&M"