I had the same problem when I set up a track bike for street use about 45 years ago. My solution was to fill the top of the fork slot with 2-3mm of auto body filler, with a short piece cut from a spoke trapped at top dead center both as a gauge and as reinforcement.

This safely pushed the wheel down, and it's been that way ever since. You can't get much more than that because you have to keep the axle and nut (or QR) faces well supported in the flat part of the dropout.

But if 2-3mm is all you need, this is simple enough and works very well.

On some bikes you might also be able to file some away at the front of the crown. Because the front wheel is forward of the crown it comes higher at the front than rear. Filing the crown to follow the rising contour of the wheel can buy you another few millimeters. This will often not work with a caliper brake, since the brake projects forward where the tire is yet higher, and often the tire will touch on the brake while clearing the crown.

Lastly, consider that there's no rule saying you need to use the same tires front and back. You rarely need more section in front (for road) so 28mm should be fine. That leaves you free to use a larger tire in back where the axle loads are higher, and you want the extra width.

Use of different tires front and back has been SOP in high performance and heavy duty auto and truck applications for decades, and serves well. There's no reason for cyclists to lock themselves out of that option.