Final push or heal

Always go the health option. Better to race underpowered than have to DNF because OCD caused you to run that last workout. My .02.

You wrote - "I realize that by taking a more careful approach I may have to suffer a little extra on the day of the race."

Not so fast my friend. If you've already put in the proper amount of time training up until now, you may be surprised how ready you'll be if you focus on health for a few weeks.

Don't risk pulling a hammy. Rest. If you injure your hamstring further, you're a minimum of 3-4 weeks to get back...and most likely longer (remember Jozy Altidore this summer).

Heal!

If you wanna workout go ahead but keep them all easy as to not hurt yourself more.

~Roland

Rest and finish is my vote.

I would rest the injury, but focus on some serious Core and light strength with the upper body avoiding anything that might hurt or stress the tendon until its healed ,being only 4 weeks out your current fitness level should carry you thru. If the tendon feels really really good I might even work in some short medium or light intensity workouts the week before the race just to get every thing loose and back in gear before the race. Tapering is great and is the preferred method of prepping for a big race but its not a hard and fast rule so if I was pretty confident that after 3 weeks that the tendon was better personally I would like to get a little work on it before the race, but if I had any dought that it wasn't 100% or very close to it then I would not do anything till the race cross my fingers and hope that it holds up or consider dropping out altogether.

Working it a bit before the race would either increase my confidence level a little going into the race or convince me that maybe this race is best left for another day. No race is worth the possibility of causing a more serious or longer term injury, there will always other races although it does suck to walk away from something you have put in so much effort getting ready for.

Good Luck, Hope it gets better for you

If you are too injured to race, there is no point in pushing yourself now. I found this video online talking about recovering from injury. It doesn't necessarily apply strictly to your situation because it is just talking about recovery in general, not right before a race, but it brings up some good points. At this point you should have done most of the work. You can sit somewhat comfortably knowing that whatever you may lack from the last few weeks of training you will be able to make up for from your base training.

Here is the link to the video: http://goo.gl/37MnEi

Hope this helps!