I thought it might be helpful for you to have the prospective of a customer on Check Point's FIPS implementation.
At best I would rate Check Points FIPS implementation as poor. First issue the lack of the ability to management appliance once it FIPS mode, no SSH or WebUI (you've already stated you are addressing this). Applying a JHFA when in FIPS mode is not documentated by Check Point and is time consuming. Features such as AV and AB don't update when in FIPS mode (open TAC case - 3+ months with no resolution). In ability to turn off FIPS mode when encountering something that doesn't work for troubleshooting etc. Extreme lack of documentation on FIPS mode.
I have seen that other vendors have a well documented FIPS mode, They provide methods for managing the appliance once in FIPS mode. They provide a documented process for disabling FIPS mode without needing to reinstall. Updates can be applied using the documented steps they provide.
I understand that applying a patch to an appliance in FIPS mode, technically doesn't make the appliance FIPS compliant any more. However, it is more important to be able to patch vulnerabilities (specifically critical and exploited ones) than to run in a compliant mode and FIPS could always be re-enabled once the patch is applied to achieve some level of compliance.
Check Point's poor or complete lack of documentation on FIPS mode leads to many customers that should use it, too not using it.