Purifying large amounts of PCR product
We had to do this frequently. What I would first recognize is that all of your current methods only work for at the small scale and that for you to purify mg quantities of DNA, you need to work with mg scale equipment.

First of all, you should examine your "upstream" process. Are you doing your PCR at scale? Typically, we have scaled out by going with multiple PCR reactions rather than one large PCR reaction. Generally the reactions max out at 50uL depending on your thermocycler. If you're getting around 1ug/10uL, scale up to a 96 well plate with 50 uL reactions and get ~500 ug of material. Make sure that you mix your dNTPs! Scale-up accordingly.

To start, the DNA Clean and Concentration is designed for really small reactions. It's much better to use the next level of purification by maxiprepping everything. The  The binding capacity of those columns go up to 1 mg. Using the QIAEX II slurry works but you should make sure that you scale up correctly. Make sure that you complete your regeneration. This protocol works well.

Alternatively you can ignore the column and just ethanol precipitate everything to remove your nucleotides. I suggest following Ethanol precipitation of nucleic acids from OWW. We had to make a lot of linear template and for most applications this works great.

As with all things related to molecular biology, there is a lot of voodoo. Some things that supposively work is to chill your ethanol mixture at -20C for at least an hour (or overnight), generally, you'll see your DNA fall out of solution and that's your sign that things are working. At this scale you should be seeing your DNA pellet; that's a good sign if things are working. While eluting anything from the columns, we would warm up our elution buffers. Thermodynamically this would make sense since it would reduce the barrier for unbinding. You would also get away with a lower residence time.

I would frankly avoid using FPLC unless you're working with gram quantities of DNA. You're not Moderna.