I will answer this in two parts. The first is addressing the HPFP and LMS tunes. The HPFP will stabilize the fueling issues with the V11 tune without a doubt. If you are looking for a plug and play solution that provides great power and you don't need to worry about pretty much anything besides maintenance, then the LMS setup is a good way to go. Assuming you are already invested with their tune. As far as performance is concerned, the V11 HPFP tune is the exact same power wise as the V11 without the HPFP. Having the HPFP will allow you to request E30 tunes from LMS which does up the power if you ask for an aggressive tune. Having realistic expectations up front are good, and the expectation should be you are investing into a product that will alleviate any fueling issues to provide a set and forget configuration. Obviously if you are experiencing issues with the V11 tune with hesitation etc, then you will see a performance increase with the HPFP by virtue of properly fueling the car.
The second part about Gearhead... His auto octane tune doesn't have fueling issues which is a direct result of how Matt tunes. I can attest to this as I run his tunes as well as LMS. I have had a heads up race at the track with the LMS V11 HPFP against another SHO that just had the Auto Octane tune without a HPFP. The results were very similar ET's. 12.799 vs 12.813(iirc) with LMS edging out GH by a hair. However, I was consistently 3MPH faster at the trap with the LMS tune. Point being is that they are both plug and play solutions that offer great performance. With the Gearhead Auto Octane tune, you don't need to datalog either, its a plug/play solution where you only need to worry about general maintenance afterwards as well.
Cost... The fuel pump is $1600... you can buy a new SCT device for $399 plus the $100 for the cost of the tune. Matt will want you to switch to SP-542 plugs, so tack on another $50.. so all in your are at $549 which is over $1,000 less for similar performance and more flexibility with the auto octane solution. The auto octane tune is far more advanced than the LMS V11 tune.
I like both tuners, as they have both been good to me. Its really up to you on what you want to do. I will say that you need to look at your goals.. if you want to run E blends and/or planning on doing more modifications such a bigger turbos, etc.. then an upgrade HPFP might be worth it.