I have once again concluded that the error seems to be persistent. A developer just linked me a change where he was able to submit while Jenkins was running its build.

However, I went back to double check the Submit Requirements and the Labels we have configured and when cross-referencing with the documentation I found this example for how to configure Label: Verified:
[label "Verified"]
function = MaxWithBlock
value = -1 Fails
value = 0 No score
value = +1 Verified
copyCondition = changekind:NO_CODE_CHANGE
But ours was defined as:
[label "Verified"]
function = NoBlock
defaultValue = 0
value = -1 Fails
value = 0 No score
value = +1 Verified
copyCondition = changekind:NO_CODE_CHANGE
[submit-requirement "Verified"]
description = Disallow changes to be merged which have label Verified: -1
submittableIf = -label:Verified=MIN
canOverrideInChildProjects = true
Which seems to allow submitting changes where the label is set to 0. I updated this to:
[submit-requirement "Verified"]
description = Only allow changes to be submitted if they have Verified +1
submittableIf = label:Verified=MAX and -label:Verified=MIN
canOverrideInChildProjects = true
And I will test whether this works better.