There is no out-of-box option or custom JavaScript to archive it but we are working on the feature of use field rule to show/hide action buttons based, it will be available with next Forms release. 

Following as i really need this feature as well.  Its becoming such an issue that i may have to scrap all the forms i've done with the new form creator and go back to all classic forms.  That would be a huge deal and potentially enough to consider leaving the LF platform altogether.

Show/hide action buttons using field rules is supported with new form designer in Forms 11 Update 3.

You can see other changes of Forms 11 Update 3 from  https://support.laserfiche.com/kb/1014413/list-of-changes-for-laserfiche-forms-11-update-3 and get Forms 11 Update 3 from Laserfiche 11 package  https://support.laserfiche.com/kb/1014263/software-versions-and-fixes-included-in-the-laserfiche-11-download-package.