If I have a choice to apply it from indoors with no sheetrock vs putting the sheetrock up first so it's packed up tight against the rock? I figured during new construction or a remodel you can apply the sheetrock but cut a small hole for the nozzle to blow in the cellulose.

Here they write "Wet spray insulation is recommended for new construction". But that may be based on having a plastic sheet interior side barrier (which would be punctured with a hole).

Installing before sheetrock behind netting is best. Only way to know if proper density has been achieved.
Drypack is difficult to do correctly, I would not try to DIY this.

Is there an easy way for a home owner to apply the netting and fix the bulging without expensive equipment to apply drywall?

I was originally planning on applying 1 inch spray foam and then adding 5 inches cellulose to fill out the cavity. I had all but decided against this and was looking to apply more expensive open cell foam over the closed. The materials and machine rental was cheap at lowes if there is an easy fix for the bulging issue.

Big Box rental machines, usually something like a Force 1 or Krendl 425 don't have the power to dense pack without stalling or plugging. Air/feed control will be difficult. You really need expensive equipment to do the process right and make it easy on yourself.

Netting is done different ways, I use an auto fire long magazine stapler which are expensive, around $400 each but extremely fast. You could use a hammer tacker, take forever, or I hear some guys staple then apply glue through the netting onto studs.

There will still be some bulging, you just roll it flat. If you value your time and the quality of an installation find someone competent and hire them.

Well that settles it for me then. It would cost me 600 worth of cellulose alone according to the green fiber calculator. That is for loose fill and not dense packed so it would probably be around 800 plus 200 for net, then more for staples and gun. Or just $1200 for enough foam to finish the job. I think I will go open cell foam.