Odd track power problem.

Most track systems benefit form frequent power taps. A volt meter won't show an issue because it  only shows when there is a heavy load (motors for the locomotive and whistle). If you run the train for a few tens of minutes, you can then immediately run your hand down the track and find the high resistance joint or joints due to the heat buildup. inspect, clean, and tighten accordingly. Use of modern ST-384 reproduction track pliers can help reform rails and ensure the pins make good tight contact.

I am certainly no expert, but having just built a fairly large layout using old cleaned track and new pins, I had a similar problem on an 031 curve near the back of the layout.  There was no rise or descent, just flat grade.

I put an extra power connection near the curve, and this was no help.

I finally pulled the two pieces where the slowdown began, one on each side, threw them away, and put in two fairly new pieces.  The problem disappeared.

I believe the problem may be that when dealing with old  track, even though you try to clean it thoroughly, there may be sections in which the inside of the pin holes are still coated in rust or corrosion, and though you use new pins, they are just sliding into rusty holes.

When you were testing the power in the troubled portion, you probably connected the voltmeter to the top of the cleaned rails, and not to the pins sticking out of each end of the trouble track section.

Just a guess.

Mannyrock

Every amateur electrician should have a few basic test tools handy. Luckily for toy train folks, it's low voltage and you can't do any harm if you screw up. You need to get a digital voltmeter (sounds like you have one) and some short (12") test leads, made with flexible #14 wire, with alligator clips at both ends. Had you jumpered the area where you have the slow down, one joint at a time, you probably would have found the resistive fault. 

Take an ohmmeter and go from each track to the adjoining track next to it. Bridging the gap. It should read zero or close to zero. If not, clean and tighten up the joint the best you can. If that doesn't work solder a jumper underneath  connecting the two.   That's why I solder all my track together. Too many high resistance joints popping up all the time.

You guys have given me some great info. I'll do some testing when I get home.

What loco are you using, which transformer, and what kind of wire to connect the transformer to the track?

Older Lionels with AC motors are VERY sensitive to inclines or "bellied" track.  The load increases very rapidly and they will slow down noticeably.  A loco with a conservative, scale-like gear ratio (which unfortunately are as rare as hen's teeth in 3-rail O gauge) will make it all the way around with almost no change in speed.  The Williams by Bachmann "Old Timer" 4-6-0 is a good example that's not too expensive.

I would get a short (6" - 12") level, place it on the rails, and go all the way around your layout.  Level the table, flatten any bellied track sections, and try to make it as smooth and level as possible.  Feed the power in at the highest point.  If all the joints are tight you should be able to get fairly consistent operation.

The trains I'm running are two Lionel 1666s and a Lionel 2020 turbine. I have a Postwar ZW 275 watt transformer. I'm using 12 gauge wire. 

 I went all the way around the track checking the resistance at the joints, but the battery is low in my voltmeter and gave me weird readings sometimes. From what I could tell, everything checked out OK. I decided to turn the train around and run it again. This time I paid very close attention to the speed and the wheels on the locomotives. It does appear I'm going to have to level the table. The slowdown isn't as noticable, but the spinning wheels at higher voltages was a dead give away. 

Knowing what I know now, I'm going to stay away from any inclines when I do the actual layout design.

Set your spirit level on top of the rails and parallel to the direction of travel.  Work your way around the loop checking for sags and bellies.  Individual sections of track could be bellied or bowed too.  Really it's not going to tell you anything that the loco itself didn't already.  A postwar steam loco makes a pretty good level! 

When you tune for consistent operation, use only the loco by itself.  A train will actually mask any problems.  For example half of the train could be on an upslope and the other half on a downslope.  So a loco will usually have less speed variation when pulling a train than it does running "light", i.e., by itself.

Spinning wheels?  What kind of load are you trying to pull?  Did you clean the track and put one drop of oil on each of the car axles?  For the 1666: if the center rail pickup wipers are still new they will add a lot of friction until a groove wears in the copper.  If the wipers have too much spring tension, they may be lifting the wheels off the rails, or at least taking weight off of the driving wheels causing them to spin.  The 2020 is heavier with a cast frame and roller pickups, so it shouldn't have these problems.  Still, the track and wheels have to be free of oil and grease for maximum traction.  91% isopropyl alcohol is a good choice for cleaning the wheels and track.  It might be hard to find in the drug store right now because of the pandemic.

With the equipment you have, inclines are not advised.  Honestly, unless your train room is very large, I don't advocate graded track no matter what kind of equipment you have.  "Over and under" seems intriguing at first, but it's a toy train thing, and fraught with problems.  On real railroads the track is quite level.  It's the adjacent terrain that goes up and down.  And that's the best way to build a model railroad too!

As a new builder, I fully appreciate all of this info as well.

Mannyrock