I have the exact same set-up you are talking about. I run my Lincoln PM255 from my Ranger 250, but it takes 2 people to start welding. The ranger is 10kw, and must be on RUN, not auto idle. The reason the mig welder does not fire off as it should is because most mig welders when starting the arc dump to open circuit voltage on the initial short of the wire until the arc is established, then maintain the welding voltage that is set. This takes place in a fraction of a second, but in that time the generator has a big voltage drop until the governor opens up. This voltage drop causes the circuits of mig welder to shut down the output.
Here is the way around it: put the mig welder voltage setting lower than 15v, and the wire feed lower than 150. Strike an arc and let the generator rev up as the governor opens up (only a second or two needed). Now keep your arc on and have your helper bring up the voltage and wire feed to the needed parameters as you are welding. Don't go too high because around 19-20v and 350-400 wire, your generator just will not be able to keep the line voltage within in mig welders limits and it will shut off the output again.
Repeat for every weld needed.
As you can see, this is very time consuming if you are welding 25 2 inch welds, but it works!
Now, I'm running 10kw output from the generator, but for your 7.5kw generator, you will not be able to go as high, and this might not work at all. I'm not sure how many kw's it really takes to light off the mig welder.
Second option: Get a small 110v welder (if your generator has a 20a 110v circuit) and use that instead of the big welder. It is also much easier to move around than the 300+ pounds of the PM255.
Hope it works for you!
Mark