Anyone use gel tape on your bars?

+1 for a bike fit - you shouldn't have much weight through your hands - longer stem maybe. Or if the fit is right then it may be down to the way you are sitting or lack of core stability. More likely a combination of all three - fit - sit - core.

Still - worth getting an assessment and fit - always sounds expensive but well worth the money.

Oh - by the way - avoid the "straight leg on pedal and plumb line brigade"!
You get what you pay for and all that!!! If you are near Newbury I'd recommend "The Bike Whisperer" not cheap but five hours of dedication from the cleats up.

I have the Specialized Roubaix tape on my Roubaix and it is great on long rides, longest so far is 8 hours and no pain. I put some on my turbo bike which had thin tape before and my hands used to numb out after a couple of hours. The Roubaix tape added loads of comfort it was very noticeable. As a number have already said the tape might be a sticking plaster to fix an underlying problem but in my experience it makes a big difference if you are riding for a long time.

I use Spesh Roubaix tape with Fizik gel simply for Flanders and Roubaix next month. They just take the sting out and will not relieve pressure points. Take a look at the gloves you have, look at the angle of the bars or the hoods. I've found that a flat smooth transition from flats to hoods and slight down pointing drop eased pressure points. Failing these a bike fit would help hugely.

Muscle pain is acceptable, back pain and joint pain is not!

It might not be a bad idea to take another look at your bike fit. I'm assuming you raised your seat and dropped your bar height to facilitate extension/arch in your lower back and alleviate lumbar pain? I rode a Kestrel Talon tri bike for 5 years and it had a very aero cockpit with a low and forward placement of the bar and with a 31 1/2 inch inseam, my seat height was pretty high with a seat tube angle of 75 degrees (most race bikes are 73). I had some problems with wrist pain and median nerve compression (numbness and tingling of the thumb to part of middle finger progressing to burning pain with rides beyond 60 miles/100K). Having a steep seat to handlebar angle puts more of your weight on your arms and hands which sounds like what you're experiencing. I think the gel tape won't hurt but IMO the cause of the problem/too much weight on your arms still needs to be addressed.

Eventually the guys at my LBS added a couple spacers to my headset and switched out my stem to one with a more positive angle which fixed things but I didn't have competing lower back issues. If you know someone who's good with fitting so you can tweak your cycling position with them or if you would prefer to get a professional fit since balancing the needs of your back and newly developed issues with your hands will be rather difficult to adjust on it your own. Eventually I switched out to a new bike, Pinarello Marvel so still race geometry but with a less aggressive cockpit than tri bikes, which is so comfortable that I can go on longer rides and have been able to increase my speed and endurance.

Well the callouses are a good start but the fact that your hands are hurting will naturally make you try to relieve the pressure on them, which you will have to do with your lower back, it's a vicious cycle (see what I did there?) Getting the balance right is a big thing, maybe you have gone too low with the stem. I can't see gel tape hurting matters, I use two layers of tape on my everyday and touring bikes. A bike fit would probably help but rather than pay silly money just ask an experienced friend to help fit you on a turbo, bike fit is easy and you will get better results by starting this way then trying minor adjustments, helps if you have a box of stems of course.

I use fizik gel pads underneath the bar tape. Here's a blog post I did a while ago on Hand numbness and long distance riding It looks at possible ways of stopping this problem

Gel tape / padded gloves will only go so far. Work on them glutes, and go to work on the core. Yoga makes my life easier. It helps me spend more time in the drops.

Gel tape is great and I love it but I think it sounds like you need to get yourself a proper bike fit if you haven't already?