There is nothing wrong with running FreeNAS on ESXi but the bad part of it is when you don't shutdown the VMs in the correct order, then all kinds of chaos can occur. FreeNAS actually has ESXi support built in.
The only thing I run on FreeNAS is Plex, I run any other VM in ESXi. ESXi is very mature and works very well. Will it solve your issue, it could make it easier for you to run an OS you prefer and then your applications in the VM. I am considering migrating my Plex jail to an Ubuntu platform. I already run Ubuntu full time in a VM so there is no additional overhead.
The main difficulty in running ESXi and FreeNAS on top of that is passing through the hard drive HBA. True that you could pass the drives through via RDM but from what I've heard, there could be some risk there and I'm not an ESXi expert. But I will say that I am now running RDM on my primary FreeNAS machine, I'm in the prosess of upgrading my hard drives to four 6TB drives and pulling the 5 year old WD Reds out. It's taking me a long time to get this done, I've been procrastinating a lot.
A little more on RDM... I tested my new 6TB drives for almost a solid week and then created a RAIDZ2 pool in my main FreeNAS box, along with my WD RED drives. I had to boot from a USB FreeBAS stick and not use ESXi because I didn't have enough HBA ports to pass through. So in this new pool I copied ~50% of my data, none of my computer backups were copied which was the bulk of my data. I shutdown the machine and pulled the new 6TB drives out. I rebooted ESXi and all came up normal. The new 6TB drives sat in the corner for about 2 weeks, I just didn't feel like foolign with them. Then comes yesterday and I felt like starting on the changes. I decided to try out RDM. RDM using just free ESXi is somewhat complicated, you need to setup the vmdk shares manually via CLI. It's not too difficult but it's a pain that you can't do it via the GUI. Anyway I searched the internet for help on RDM and found it, read it, made my own changes, and all seems to be working. The good part is the pool imported without issue.
Well you should give VMWare Workstation Player a test drive and it will give you a feel for ESXi.