"Are there any concerns with running a WYE wound motor on DELTA power, or a DELTA wound motor on WYE power?"
No.
As long as there are no connections to ground within the load, the load cannot tell if the source is Y or is ∆.
For practical reasons, most motors are designed as Ys.
Yes, there is indeed an internal "star point", which otherwise would be a neutral, but this point is seldom, if ever, brought out to the motor's connection box. For, if it was, it would be the junction of what would be T10, T11 and T12.
(In rare cases, motors are supplied as "12 wire", with T10, T11 and T12 brought out, but most are supplied as "9 wire", with T10, T11 and T12 as an internally connected point, and not brought out).
When one changes a 208-240/480 motor from the higher voltage to the lower, T4, T5 and T6 are connected, and are insulated from all the others, and T1, T2 and T3 are connected to T7, T8 and T9, respectively.
The source is then applied to T1, T2 and T3, as is usual.
There remains, then, two "star points", namely, T4-T5-T6 and what would be T10-T11-T12, both effectively isolated from one another.
The motors are designed with this in mind, and it is not possible, nor is it required that T4-T5-T6 be connected to T10-T11-T12.
Polyphase systems have for more than a century been designed with ∆ and Y being interchangeable, through the ∆-Y transformation.
For practical reasons, most primaries are ∆, while many secondaries are Y, but a lot are still ∆.
It really makes no difference, for as long as there are no grounds, ∆ and Y are interchangeable.
The ubiquitous North American 120/240 ∆ residential power distribution scheme presents certain problems, as there is an implicit ground.
When one constructs an RPC, there becomes a virtual neutral, N', at the "star point" of the idler motor, this virtual neutral being elevated from the real neutral, N, by 69 volts.