Here is the .25-06 Remington Data:
And here is the .270 Win data:
That puts your load data for the 6.5-06 somewhere between 48 grains to 57 grains, depending on bullet weight. Realistically you won't GET to 57 grains as the .270 has a larger bore making the pressure lower with that powder charge. I'm guessing you'll end up around 53grains for a 140grain'ish load, but someone with QUICK-LOAD could pin it down more precisely.
That still feels pretty 'vague' to me, so the next thing to do would be to find reloading data for the 6.5-06 with powders that are similar in burn rate to RELODER 23. Here is a burn rate chart. Sadly, Reloder 23 isn't specifically listed, but Reloder 22 and Reloder 25 are shown, so we can 'guesstimate' where Reloder 23 would sit in there.
So it looks like a comparable powder would be VihtaVouri N165 and IMR 7828.
Finding reload data for IMR 7828 in 6.5-06 is easy here:
https://www.hodgdonreloading.com/data/rifle
So
it looks like you'd be safe starting at 45 grains with a 143 grain Hornady ELD-X and working from there, depending on the velocity you get.
I tried to find reload data for VihtaVouri N165 as it was also about the same burn rate as Reloder 23, but they didn't show the 6.5-06 in their data.
You didn't say what bullet weight you were working with so I'm just "assuming" a popular 'heavy' bullet for the caliber (143gr in 6.5-06). If you go to a lighter bullet, well, then this doesn't really apply and I'm out of ideas for you.