I've been using a 21c tubular front with 23c clincher rear for over 9 months now and it works well, but the tires have been as close to the same construction as possible to minimize the differences of traction or compliance between the F and R. In the past I've also used 23c fronts + 25c rears with no problems.
For example, right now I'm using a Vred Fortezza Pro 21c tubular with a Fortezza Tri-Comp 23c on the back, since the casing and rubber are very similar if not the same. I would also use say a Vitt Corsa CX with an Open Corsa CX, or a Schwalbe Ultremo clincher & tubular, or two similar Conti's, etc. But I wouldn't think two fairly different designs like your Conti Force + Velo Record is a good combination, but who knows (?) - they could work well together too.
The main reason I do this is not so much the width differences but for the safety factor of a tubular up front in case of a flat or blowout on a high-speed descent, and the cost savings of not having to replace a rear tubie when it flats, which is where I get 90% of my flats. Handling and performance-wise, there is no problem with this clincher/tubie combo.
As for PSI's, I determine that based on my weight, the particular tire's behavior at certain PSI's, and whether it's mounted F or R. In this case with the Fortezza's I use around 130 F/130 R, +/- 5 PSI depending on conditions.