Seems like options include, suppressed 30-06. Though if this not getting traction Ill have to agree the 25-06 with a premium bullet offer what you are asking for as well.
If you just want a new rifle Id go either 6mm Creedmoor or 6.5 creed moor. Suppressor still good consideration with a 6.5 or a 6mm Creedmoor IMHO.
In any case choose a premium bullet. All copper is worth a look IMHO.