Encrypted drive + shutdown is a defense against a specific Evil Maid attack, cold boot attacks. It is not a very expensive attack to run; for the cost of a can of compressed air, and a USB drive, anybody sophisticated can run this attack. https://en.wikipedia.org/wiki/Cold_boot_attack
Sorry to sound defeatist, but if you had been relying on IOMMU to save you, the trivial "plug anything into a USB port and you have CPU JTAG access" attack has always been possible. (Never mind that IOMMU implementations aren't guaranteed to be bug free.)
In the face of that, what do you do?
With this knowledge, all I really can do is stay up to date and patch-patch-patch. Have a travel Chromebook for leaving in hotel rooms, but ultimately I just have to know that it's not enough, especially against a CIA-grade Evil Maid, or an Evil Maid that's able to factor 4096-bit prime numbers. (That last one's not theoretical, either. It was revealed a few weeks ago that TPMs in Chromebooks and other hardware was generating weak keys, leading to cloud-factorable 4096-bit RSA keys.)
A less-sophisticated Evil Maid can still physically steal my laptop for pawning, and even if they can't get my data, I've still had my laptop stolen. Not-being-defeatist, I backup my data, although that has a totally different set of security concerns over the Internet.
That mitigation is useless against Evil Maid. There are much more sophisticated mitigations (using a TPM to measure the boot, and then do something akin to TOTP in order to allow the user to actually verify the state of the machine) which actually could protect against Evil Maid almost completely (assuming you don't have something like Intel ME that cannot be verified by the TPM).
"Once you have physical access it's game over" is a very common response to these discussions, and I find it incredibly defeatist. Of course physical access means that the "clock is ticking" until your data is compromised, but sufficient protections can dampen the impact or increase the difficulty.
For example: IOMMU protects against DMA-based attacks, something that was impossible to protect against several years ago. This doesn't mean that someone cannot launch other attacks, but it does mean that the trivial "just plug anything into a USB port and you have DMA" attack is no longer possible.