How Smart is Auto MDIX?

I'm finding this is a bit of a tough problem to Google, but it is a problem I can't currently troubleshoot because there won't be power to the facility with the installation for another few weeks. TLDR: Can Auto MDIX figure out miswired ethernet that is neither straight-through nor a regular crossover?

Essentially we have 50+ runs of shielded Cat6A from client to patch panel (link to exact patch panel), and on the punch down block there were color designations for T568A or T568B, of which T568B was chosen. Upon running each cable through an RJ-45 tester, it was discovered that each of the RJ-45 connections way down on the other end were not wired to either T568A or T568B standard. The actual pinout order of the wires is shown below (I've also included T-568A/B for quick reference):

Pins	T-568A	T-568B (@ Block)	Actual (@ RJ-45)
1 - TX+	White/Green	White/Orange	White/Orange
2 - TX-	Green	Orange	Orange
3 - RX+	White/Orange	White/Green	White/Green
4 - TRD2+	Blue	Blue	Green
5 - TRD2-	White/Blue	White/Blue	White/Brown
6 - RX-	Orange	Green	Brown
7 - TRS3+	White/Brown	White/Brown	White/Blue
8 - TRD3-	Brown	Brown	Blue

So now I am wondering ultimately if the cables will need to be re-crimped at the RJ-45 ends, or re-punched at the blocks. The switches we have everything hooked up to do indeed have Auto MDIX, hence the title of the post. Exact switch model link here: Cisco SG220-26 and Cisco SG220-48. So, with the pinouts shown in the above table, we are not sure if we will have to change anything. For further context, our requirements are less than 100Mbps, the important part of the application was the shielding because there will be a non-trivial amount of EMI. So we don't need a ton of throughput, it just needs to transmit packets.

Apologies if I sound like a newb, I am just beginning my journey into Networking :) Fantastic community here, I have been lurking quite a lot.

Thanks.