OK... you've defined your requirements:
"I would really like to be able to remove bales from the back of my pickup, pick them up off a flat bed trailer and stack them at least two high for storage."
My opinion is that you need an LA853 loader to do this. Your most CRITICAL requirement is to be able to stack 2 high. This means lifting a heavy bale very high, hay spike required, my opinion, not pallet forks, and LOTS AND LOTS of
ballast. It's the high lift that defines the hydraulic power you need. So, look at the specs at MAXIMUM LIFT HEIGHT.... that is what will determine what loader you need.
Let me be explicit, I will NOT lift a bale high (and 2 bales high is very high) UNLESS I have a bale on the rear of my tractor for ballast in ADDITION to other ballast weight that I have, including fluid filled tires. Then, it's a breeze. I am sure that on totally flat ground with good traction and 4WD you can do it with less ballast, but farm/ranch conditions are NEVER that way... it is very often slick, uneven, rainy, slanted ground when you MOST need to use the tractor.
Fundamentally, your requrement regarding hay bales is the same as mine was..... the 5030 and LA853 loader are exactly what I need and are safe, but I wouldn't want to do it with less loader or less total properly distributed weight. My equipment is very capable of doing that job and safely, but I can tell that for me anything less would be a constant struggle and worry about doing something wrong that would quickly turn into a serious problem. For me, it is a perfect functional match.... not oversized for the job, nor undersized... and I think I know the difference both ways.
It's a lot of money. If funds are less important, then I can highly recommend my set up. If you need to use less tractor and can live with pulling bales out of your pickup and off the trailer with ropes (as I used to do), and not stacking them, then I, again, recommend you look into a 2 wheeled hay buggy that can be pulled behind either a pickup or your tractor on the trailer hitch. If your 2 bale high lift requiremets are firm, then you MUST get a loader capable of lifting 1500 lbs to max height... remember that when first baled hay weighs a lot more than when fully dry... and when rained on it again weighs a lot more... from my experience, consider 1500 lbs the weight of a round bale, leave some room for weight of the quick attach, hay spike, etc. and you will be OK.