Further to my earlier message, I just gave my Dawes her wash 'n brush up (I wash her every year whether she needs it or not) and took the time to see how it compares with yours. For the record, if I straddle the frame wearing trainers, it just gently rubs the old undercarriage, which is probably not Best Practice, but it's never worried me, and certainly doesn't stop it being a very enjoyable ride. Do note, tho', how low the saddle is, and also the minimal front-extension on the handlebar stem - it's the shortest I could get.
Mind you, I would just add that from your description, I personally would be tempted to chuck that one back in the water (or, to put it another way, put it back on
ebay with a slightly OTT description featuring key phrases like 'fixie' and 'steel is real' - you might get more than you paid for it) and look out for/bide my time awaiting something a bit nicer. A tatty-but-serviceable 531, eg.