The replacement plugin was a 7B50.
Great idea about the full loading! That makes sense why the two verticals would work since the middle slot was empty. I'll try that when I get home.
Just install the 7B53A into the middle slot then for a full load test. Measuring AC ripple on the power supply outputs should be sufficient but I often check the power supply inputs as well after estimating what their ripple should be just to see if the input capacitors have become marginal without measuring them directly which is more difficult.
If the power supply is marginal, then it is not uncommon for some plug-in combinations to present too much load leading to problems. Some plug-ins are worse than others in this regard and so much so that it is possible to exceeded the rated power supply output and/or the mainframe cooling capacity with some configurations.
With that said, any combination of 7A18s and 7A22s and a 7B53A or 7B50 should work fine in a 7503 despite it being one of the early 7000 mainframes.
How did you end up with a 7B50? Its 100 MHz replacement, the 7B50A, is much more common as it was produced as a less expensive alternative to the 100 MHz 7B53A for a long time. The companion to the 7B50, the 7B51, was only produced for a short time and then both were replaced by the 200 MHz 7B70 and 7B71. One of my 400 MHz mainframes came with a 100 MHz 7B50A which I paired with a 400 MHz 7B85.