A bit of reading (Birmingham Proof House site is good) will help explain "proof" and "in proof" better than one post but here goes:

A gun is in proof if its chambers are, its bore is no more than a few thousandths different from, and it gauge is as indicated by the information given in the proof marks on the barrel flats.

The chambers should measure 2.5 inches based on what you have described but not been able to show in a picture.

Look at GJZ's photo to get an idea, confirm what you see on yours, etc. (Like his 12 over a "c" in the diamond explains the gauge at proofing.)

Opening up chokes will also take a gun out of proof as I read the provisions.

If done in the UK, sleeved barrels are so marked at the time of proof.

This gives you an idea why evaluating proof and current condition is important.

Having a gunsmith schooled in English bests look at your gun, take the appropriate measurements and give them to you would be a tremendous help in selling your piece. For example, such a professional would have been able to tell you that the barrels were replacements.