Now if you are really determined to purify your own technical grade borax into the equivalent of reagent grade, then I would suggest incorporating the following suggestions:
First, boil your solution. And do it for a while, like an hour. It does not have to be saturated while you boil it - that would be a pain as the solution would want to crystallize out as you are boiling it. And it doesn't have to be a hard boil, just keep it near boiling for the hour. The reason is that you want to try and use the high pH and temp of the boiling borax solution to hydrate any silicates in the borax. This will help them drop out of solution and make them easier to filter out.
Second, filter your solution to remove insoluble matter. Get yourself a large (like a 20 or 30 cm diameter) Buchner funnel and some glass fiber filter paper. The Buchner funnel can readily be found on ebay for less than $20. Get a glass filber filter paper like Whatman GF/C which has a pore diameter of about 0.45 um. This will remove all particulate.
Third, after you've done your leach to remove the chloride and other things that are more soluble than borax, use enough water to dissolve your remaining borax so that it makes a saturated solution at a temp of about 80 to 100F. This way, after you've boiled your borax solution, you can let it cool down some to make it safer to handle, and then filter it with the Buchner and a vacuum to help it pull through the filter. So filter it when it reaches about 125F and the borax will stay in solution and not clog the filter.
So now you have a filtered solution of borax, with no insoluble solids. Since we dissolved enough borax into the liquid so that we would reach saturation at about 80F, we will get some crystals of borax precipitatating out of our solution when we get below 80F. Go ahead and cool it and hold the temp at your 63.6F. That's the hard part of your procedure - hitting that temp and holding the solution there until all the borax drops out of solution. Constant agitation from a magnetic stirrer would be good here. Let it sit at that temp for a significant period with the excess crystallized borax in the bottom of the container. When you think it's been long enough at 63.6F, then decant the solution into another bottle and store it at a temperature that is higher than 63.6F.