In reply to BStar:
I'm currently trying to rid myself of double tennis elbow, which I suspect was brought on more from excessive DIY and misuse of a flexbar (buts that's another story) than from actual climbing.
After getting an ultrasound and seeing an orthopaedic specialist, the best advice I came away with was to regularly do activities which lightly use the injured tendon until you feel a small level of soreness, this will encourage your body to pay attention to the tendon and promote healing. For me, this was light-ish steep climbing, (which may not be ideal for you if you have golfers elbow too) which caused no direct pain while doing it, but left my elbows feeling sore after a couple of hours. The next morning the elbows would feel noticeably better and this happened every time I climbed as long as I didn't push too hard.
The specialist told me that for the last couple of decades there have been numerous treatments developed, ultrasound, laser, steroid, acupuncture, heat, cold, you name it, but the only thing that can repeatably be shown to help is light use of the affected tendon to encourage healing. He said to indulge in any of the other treatments by all means, (I like to heat, massage, mobilize and stretch occasionally) but it will most likely only make you feel better about being proactive rather than definitively helping the tendon.
I've gone from being unable to pick up an empty glass at arms length to being able to hold a full bag of shopping at arms length in 4 months, so it has been working for me, good luck!
EDIT: I should add that exercises like the broom handle one could definitely be considered as light use of the affected tendon, I've heard good things about them
Post edited at 12:26