I feel your pain.  Literally.  I also have "double jointed" thumbs - I have to be really careful about supporting the joints while I'm using the tip as a tool.  One technique for thumbs that works well for me is to use the rest of my hand to support the thumb - curling the other fingers into a loose fist and having them act as a shelf - my fingers support the base of my thumb and still allow me the sensitivity of using my thumb for deep tissue work.  The thumb is flexible from the top knuckle to the tip, but is supported the rest of the way.  
 
I have skinny long fingers, so techniques that allow me to use more than one finger at a time help support them.  Also paying attention to the angle of my wrist - never breaking the line of the wrist to the hand, even to get more pressure.  Keeping that straight unbroken line through the hand for deep work lets me use the weight of my body to get deeper or more pressure, without compromising my fingers.  Never hyperextend the wrist -hahaha, ok, reality check, but at least try not to for the deep work.
 
It sounds like you may have to set some boundaries for your own safety and comfort.  If a client doesn't want you to use the tools you have available, and to do otherwise would compromise your body mechanics (and therefor your means to do this work), you may not be the right practitioner for them and they may not be the right client for you.  I learned this first hand from thinking I could work on anybody all the time - as it turns out, my ideal deep tissue client is not a 300lb former semi-pro football player.  On the other hand, communicating with the client may help - maybe they are averse to elbows and knuckles because they've had someone slip and crash into their bones.  It may be that you could negotiate an interactive testing of the waters with their feedback.  
 
And practically speaking, ice after working helps with swelling and inflammation.  And I personally have started taking a supplement geared towards relieving arthritis and healing connective tissues.  Its got the usual joint stuff and also turmeric and ginger which help with inflammation.  Hope this helps - AMY