Is it normal for the washer drain hose to loop up higher than the machine?

You're completely fine leaving it as is. Washer drain pumps are centrifugal and built to handle quite a bit of head pressure. Virtually every older top-load Amana is rated to push water up 6 to 8 feet from the floor without breaking a sweat, so going just an inch or two above the machine cabinet won't strain that motor at all. In fact, having the hose loop up that high is acutally a good thing. If a drain line sits lower than the water level in the wash tub, you risk **siphoning**, where the tub accidentally empties itself as fast as it fills. That high arch keeps the water where it belongs untill the pump actively kicks on.

Zip-tying the hose to the standpipe was the right call to keep it from kicking out during the pump-out cycle. Just make sure you didn't shove the hose down too far into the standpipe or seal the connection with tape. You want about 4 to 7 inches of hose inserted, with an open gap around it so air can breathe. If you push it down past the P-trap or seal it up tight, you'll create drainage issues. Run a couple of normal loads to confirm your connections are dry, then pull that towel away. As long as your total rise from the floor to the top of the hose loop is under seven or eight feet, your setup is completely safe.

Those old Amanas are absolute tanks—nothing like the plastic junk they sell at the big box stores today. Back in the seventies we used to run these straight up into heavy concrete utility sinks, often five or six feet high, with a cut-off pair of pantyhose rubber-banded over the end for a lint trap. Never burned up a single pump. Only thing I'd watch is that old black corrugated hose. Those original factory hoses love to dry rot right at the high bend after twenty years. Give the curve a firm squeeze with your thumb. If it feels chalky or brittle, spend five bucks on a fresh reinforced hose before it splits during an overnight load.

Wait, so if the hose goes up that high and then drops into the standpipe, does some of the dirty water flow back down into the washer when the pump shuts off?

I realy don't know much about plumbing or how the pump works inside, but wouldn't gravity just pull whatever is left in that high curve right back into the tub? Or is there some kind of flap or one-way valve inside that stops that from happening? Wondering if that causes bad smells over time.

Agreed, height isn't an issue at all for those pumps. Just keep an eye on the arch itself. When hot wash water pumps thru, that corrugated plastic softens up, and without one of those rigid plastic U-bend guides, the top of the curve can start flattening out and kinking under its own weight over time. Also make sure you didn't crank that zip-tie down so tight that it's crushing the ribs of the hose. Just snug enugh to keep it from bucking out of the pipe is all you need.

I'm brand new to tinkering with laundry setups and this is so cool to learn about! Since you have this running down in a basement utility space, does anyone here use those little battery-powered water sensor pucks on the floor by the drain?

I just moved my first washer into an unfinished basement and I'm terrified a hose will slip out and flood the floor while I'm asleep upstairs! Are those cheap leak alarms actualy loud enough to hear through the floorboards, or do they just constantly false-alarm from dampness?

Quick update — thanks everyone! Good to know these old Amana pumps can easily handle the height without burning out, so I left the standpipe alone. I did take the advice about the hose softening up and grabbed a rigid plastic U-bend guide to keep the arch from kinking. Ran two loads with hot water today and it drained perfectly. Towel is dry!