Well, you are quite right about medications - they just give you a lot of other problems in place of the one you have and only partially work anyway. Besides, if the cause is the stress, then reducing the stress is really the only way to treat the problem. However, I have a couple of ideas for you ...
The first concerns emptying your bladder - do you do this on a regular basis? If you can manage to beat your bladder to it by, maybe, emptying it yourself in the loo very 2 hours, there is a good chance you could have it pretty empty so if you do have an urge it would only be a small amount and small amounts are easier to deal with . You would have to notice when things happen and see if there is a schedule you could set up to keep the bladder empty and stop if draining large volumes without warning.
The second is just another way of catching the output. Diaper are very popular in North America and seem to work well for many but large voids are very tough for a diaper so an alternative might be worth considering. We call the condoms or sheaths but in the USA they are called external catheters. These are self adhesive and roll over the penis and remain in place for 24 hours. You can attach a leg bag for daytime and a bigger bag for nighttime if needed. A 750ml leg bag would allow you to catch sudden voids and drain them out later. Have a look at
http://www.us.coloplast.com/products/continencecare/pages/default.aspx to see the sort of things available. You can even order samples from them. I have been using their Optima sheaths at night for a while now and they work fine and use then in te day if I am going far from home too.
A final note - don't stop drinking enough and stronger urine will make things worse.