If you only need to carry one bottle then what about your rear centre jersey pocket. When I ride my duallie which only has a single cage due to pivots I carry a second in the jersey and drink that one first to lighten things up. For you the problem will be if you use 750ml bottles as that will get quite heavy and also the fluid will heat up more quickly. (I carry 600ml bottles) if you only need 600ml the jersey will actually be fine.
Is your frame issue is due to size and space? Because if you have space but just not mounts, then see an engineer and you can get it done, that is, installed. If it is carbon (is that carbon?) see a specialist asthat does carbon repairs, there's a few around, just can't remember as I type right now, but if you are desperate, pm me and I will get u details, may cost a few bucks tho.
Good luck.