Daisy chaining switches hurts latency as all switches' delays in a path add up. Performance doesn't seem to be your problem though as you're still on Fast Ethernet.
Chaining is also the worst topology reliabilty-wise. Any switch in a chain failing breaks the chain.
Deep (long) topologies also exclude redundant meshing using a spanning tree topology. RSTP/MSTP have a design limit of seven hops.
Ethernet is most comfortable in a tree - a center switch with all the other connected in one or at most two layers. If redundancy is required, use two center switches and two links to each of the others with spanning tree configured correctly (the center switches need to be root and standby root switches, with the lowest and second lowest bridge priority values).
Any form of ring or meshing requires a spanning-tree protocol or similar. Without that, the bridge loops causes a broadcast storm and brings down the network, usually in a matter of seconds. In other words, loops with unmanaged switches are fatal.
Using twisted-pair cabling, the longest legal link is 100 m (90 m solid-core + 10 m flexible patch cable). Longer links can be realized with fiber (multi-mode is good for a few 100 m, depending on cable grade and speed; single-mode runs for at least 10 km).
Is it possible to home-run the furthest switch to the middle switch and then from the middle switch back to the first?
Yes, that would be an improvement, but it requires STP.
If your cabling permits, connect all other switches to switch 8. If there's just a single host (or two), you can omit their switch and connect them directly, as long as switch 8's port count is sufficient. Use fiber for the runs longer than 100 m. Generally, try to keep the hop count to the center as short as possible - improving latency and removing single points of failure.
If you're restricted with budget, try to come closer to that goal. Depending on the cable lengths and count, you could e.g. connect switches 4-7 and 9-12 directly to 8, elect switches 4 and 12 as intermediate switches and connect 1-3 and 13-15 there.