The question for me is... is your diagram just a quick mockup to give us an idea of what you want to do or is everything already physically connected that way?
A high-level, straight forward approach for accomplishing your goals would be:
Create VLANs on the PFsense LAN interface
Consolidate down to 1 managed switch and connect it to PFsense via a trunked interface
Connect everything to the managed switch
Configure firewall rules to control access as necessary
There's no way to accomplish everything you're looking for as currently shown in your diagram. If you keep the transit network, you can establish connectivity by moving your servers to one of the other switches, but that would mean your VLANs would be terminated on the middle L3 switch and you'd lose inter-vlan firewalling capability. This would be the favorable design from a performance standpoint, but you lose granularity in your access control.
If you want to keep the 3 switches and require inter-vlan firewalling, you can still accomplish your goals, but it would require a re-design and managed switches. You'd need to:
Create VLANs on the PFsense LAN interface
Re-configure the link between PFsense and the middle switch as a trunk
Trunk the two outside switches to the middle switch
Move your servers to any of the three switches
If everything is in close proximity, personally I would consolidate down to one managed switch to keep it simple.
Regardless of your design choice, in order to fulfill all of your requirements, all roads lead to managed switches and a re-design.