Tubes&More _did_ "tell" you this one is P-P, though very subtle. See attached.
Tubes&More does NOT make it easy to find SE iron.
This filter link is supposed to find SE, but in fact it finds a lot of P-P iron which mentions SE alternates.
This sorted filter shows that the true SE iron does not appear until the $40 range. There is some sense to this. For the same Watts, SE iron will be 3X-4X the size/weight of P-P iron.
Impedance 4K or 5K makes no difference. Wider differences are often done. A quick analysis of that Rick-Tone suggests 7K as a "best loading". However this is clearly NOT aimed at "maximum loudness" "stadium blaster". Design is actually constrained by use of two commodity 120:12 transformers back-to-back, with double sag. Ideally this is 330V DC, but actually 300V no-load and under 280V at 35mA load. Power Output is 3 Watts at best, and maybe 2W with 4K-5K loading.
Any "Fender Champ" OT is quite suitable. Mostly not cheap. Any old-old radio *with power transformer* and one 6V6 has a 5K OT, though finding one in working condition could mean buying and shipping a lot of heavy junk. "AC/DC" radios with 35C5 50C5 etc outputs are NOT suitable.
A possible alternative to new-made output transformer is to scour eBay for "Epiphone Valve Jr" OTs. It was one EL84 at much higher voltages. There was a fad to rip-out the stock iron for other iron (assumed better). The rip-outs often appeared on eBay, so many that prices fell. I do not know if this fad is still running, if it may still be a buyer's market.