Boil volume/late extract addition

So I've just purchased my 5 gallon kettle today and figuring out my boil off atm. My kit should be here tomorrow and this is what I was planning to do:
3 gallon initial boil
steep specialty grains
hop additions with a 60 minute boil
add LME into the primary along with the wort

originally I wanted to add the LME to the boil, but looking at my tiny 5 gallon pot with the 3 gallons of boiling water atm (to calculate my boil off) I realize how little headspace I have so I'd imagine add that LME in there and I'd be SOL.

Suggestions and critisims are VERY much welcome.

BTW: Working on an electric stove (I get to a boil, but defiantly not vigorous) and a propane burner is out of the question (at a 3rd story apt with a tiny patio, kind of afraid to brew out there). Forgive me if this question has been answered numerous times, I suppose my searching skills are not up to par

Edit: I suppose my main question is: would you rather decrease the inital boil volume and add that LME into the boil and/or would that affect the outcome of the finished beer significantly?

If you reduce your initial water volume to 2.5 gallons, you'll be around 3 gallons once you add all your extract, assuming you're brewing a moderate gravity beer with 6-7 pounds of extract.

This is what I do in my 5-gallon boil pot, and my pot has plenty of room to handle any foam generated in the boil.

I would suggest add the LME at the end of the boil (60 min) and stir thoroughly. I don't think you want to add unsanitized LME to your carboy or bucket.

It will be most likely be hot enough to sanitize it but it will cool your wort more quickly.

Did some reading and realized that the sugars are necessary for the hops to do their thing and ended up doing what CarboyBoy said. Thanks to you both, first batch came out a sucess! Enjoying a nice Honey Cream Ale atm.