You could stop using a text field and start using a formula as well. That way you can guarantee the fields always match, then there'd be no reason to even have a validation rule to begin with. That does however, depend on what values you expect the field to have when the record type is different.
Alternatively, throw together a process builder to enforce the rule. If the record type is of the specified Id, update the value of the field to match the value in the desired record. Again, this would force the field to have the correct value meaning you don't need a validation rule (and you're employees can save time by not doing 1 extra copy/paste)
In response to your comment about not being able to use a PB. You actually can use a PB for this. Combine both your field update and your email alert into a single PB. Put your field update in the first branch. Use the record type as the criteria for executing the update. Then, you should see a "Stop" to the right of your field update. Click on that and select "Evaluate Next Criteria". Then, in the second branch, set no criteria and put in your email alert.
This way, if the record type is incorrect, nothing happens and the email sends. If the record type is correct, the field updates and the email sends.
I was able to find this screenshot on the interwebs: