Press ups! and lots of them! I know that's what the VMax ladies used to do. Their coach recommended that they could do at least 10 FULL press ups - ie NOT knees on the floor but feet and hands only.
Not only does it work the pecs, shoulders and upper back, but helps the core stability muscles which are important for the "cross-crawling" techniques required for efficient turns, but it will also help to support your back in the long term.
Lots of stretching before and after your sessions will help as well. If you need any details on these feel free to PM me - I'm an osteopath by the way, (with 11 hours of tunnel time) so I'm not talking off the top of my head!
Have fun - Bedford rocks!!
Fi x