There is a engineer and pilot on pprune who has a few aircraft who will give you a plane dry for a USA rate to do with what you want as long as you get it back for a 50 check.
No doudt he will PM you if you ask nicely.
AT who owns OBA is a fanny of the highest order, rule 5 should be applied. ie find out when he is holiday and go then or stay well away. There is no prob with OBA just AT when he is there.
Hours at night are not such a bad thing in FL it is 100000 times safer doing night hours in FL in a SEP than in the UK and might do you a favour for ATPL issue.
But FL is boring as hell for hour building especially if your trapped with wet rates which mean it costs an arm and a leg if outside 1.5hours flying from one of the FTO's
If you can find some school which will give you it dry at tacho hours and bumble around FL at climb out speeds paying 75% for ever hour logged thats the way forward.