You can get a Dell R340, brand new, with 32GB of RAM and a 3.7 GHz (5.0GHz turbo) 8 core Xeon for about $2250 with a 240GB boot SSD, and a second for $120. That would give you your Raid10 SSD setup. The only real limit is that it is a 1u server and thus cant run more then 4 drives. The 2u servers are mostly running EPYC processors, which you have expressed disinterest in.
I'd offer to send you one of my old servers, but they are all set up for multi threaded workloads, and thus have high core count/low clock speed setups, and are all generations older then what you have currently. How much RAM can either current box take? There may be some of us willing to buy and ship you large quantities of DDR3 RAM sticks, or may have, say, 48-96GB of the stuff laying around. Just saying......
Alternatively, the R240 can be had with 16-32GB of RAM and the same processors as the R340 for a cheaper price. It has no hardware RAID controller, but you are not going to use that anyway.
So, best plan, get a pair of R240 servers, one set up with lots of RAM and a E-2236 CPU (6 core 12 thread 3.4 GHz, 4.8 GHz boost) to replace BOX 1, the other set up with a Xeon E-2288G CPU (8 core 16 thread, 3.7 GHz base 5 GHz turbo) for your PHP box 2, then take one of your current boxes, fill it with the HDDs you need, and use it as a NAS for box 1 and 2.
EDIT: both servers with 32GB of RAM each would run you about $2700. Wouldnt come with SSDs, and instead are outfitted with 1TB HDDs, but that would give you everything but storage for a little more then half your budget. Buy a couple of large HDDs for your old BOX 1/2, turn it into BOX 3, set it up as remote storage for the new box 1/2, and call it a day. It would give you a lot more breathing room.
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