I talked to Lundahl Last night
it seems that LL3720 is a good match. Mr Lundahl will make a 5K version for this project.
https://www.lundahltransformers.com/wp-content/uploads/datasheets/3720.pdf
From Lundahl
We are developing a new output transformer, LL3720 (6k : 8 ohms) specifically for single end application.By applying some tricks when winding the coils, the capacitive coupling between primary and secondary sections are minimized, which results in a better high frequency response. The transformer is suitable for triodes with plate resistance between 1 and 2 k, and thus matching DC currents from 30 – 40 mA up to 70 – 80mA. A data sheet for the LL3720 will follow shortly