Drauk,
I think my point is plainly obvious, don't climb into the TMA.
If you have mode C on and are sqwauking 7700 you may well alert controllers operating at a different unit not aware of you. However I imagine especially if operating single handed you will have little time to change the code and many light singles do not have mode C and from personal experience as an ATCO will have enough difficulty getting a Mayday call out without advising that you are climbing.
200ft may make the difference yes fair enough but what if its more , you are not necessarily concentrating on the additional altitude to which you are climbing, a climb into the teeth of large aircraft is not a good idea.