If I wanted a 338-06 and was starting from scratch with $1,500, I think that I'd consider this:

$500 - for a used CLR in 270 or 30-06.
$250 - for JES to rebore it to 338-06.
$600 - for NULA to install an upgraded stock, trigger, and safety.

$1,350+/- leaves 10% of your original budget to cover contingencies.

I would then settle on the one .338" bullet that does it all and does it well, the 210 grain Partition.