As for an RNAV approach with a non approved GPS you are out of luck.

As far as getting into your airspace with ATCs help that depends. You would need to find out what their minimum vectoring altitude is in that area which is not published but they should tell you if you ask. I would be willing to bet though that it is somewhere higher than 700 feet. If it is somewhere close to that you can always ask for vectors to your airport and then ask for lower in the hopes of glimpsing the airport but youd need to be prepared to go to an alternate.

Best bet by far is that if you can afford a plane you can afford a used garmin 430 or similiar off ebay and get it installed, it will save you hassle.