Whiter whites with Sabattier effect

Hello, I've started doing enlargements recently and yesterday, tried my hand at the Sabattier effect (exposing the paper to white light during development to create a partial negative image on the paper due to masking by the image forming on the paper). I think I more or less got the hang of it, with 2 second exposures being the most effective, however I was left with the problem of the whites in the photo being left rather grey. Using shorter exposures (1 sec) helped but the effect was too subtle.

I also tried using contrast filters (Kodak Polymax). This helped a lot, but still, I'd like the whites to be whiter. How can this be done? I suspect bleaching might be the way to go, although I might lose the blackness of the blacks without further toning. I tried using household bleach, but ended up losing the entire image.

If anyone has a suggested technique, please let me know. I'll paste below 2 pairs of images. The first being the raw scan of the print and the second, a digitally tweaked version of how I would like the print to look.

All the best!

Raw scan of print with no contrast filter and 2 second exposure to room light during development:

Adjusted in software:

Raw scan of print with Polymax filter #5 and 2 second exposure to room light during development:

Adjusted: