You could use toString and parseInt method, that basically are doing the same thing of the methods you mentioned in the link:
var hexString = "4b3fc1400";
var b36 = parseInt(hexString, 16).toString(36); // "9a29mgw"
And to convert it back, you just need to do the opposite:
hexString = parseInt(b36, 36).toString(16); // "4b3fc1400"
The only problem with your string, is that is too big to be threat as number in JavaScript. You should split them in chunk. JavaScript's numbers are accurate up to 2^53 (plus sign), so the max positive number you can handle is 0x20000000000000 (in hexadecimal, that is 9007199254740992 in decimal); you can use the accuracy to handle the chunk:
var hexString = "37c1fbcabbc31f2f8d2ad31ceb91cd8d0d189ca5963dc6d353188d3d5e75b8b3e401d4e74e9b3e02efbff0792cda5c4620cb3b1f84aeb47b8d2225cd40e761a5"
var b36 = "", b16 = "";
var chunk, intChunk;
// 14 is the length of 0x20000000000000 (2^53 in base 16)
for (var i = 0, max = 14; i < hexString.length; i += max) {
chunk = hexString.substr(i, max);
intChunk = parseInt(chunk, 16);
if (intChunk.toString(16) !== chunk) {
intChunk = parseInt(hexString.substr(i, max - 1), 16);
i -= 1;
}
b36 += intChunk.toString(36)
}
// 11 is the length of 2gosa7pa2gv (2^53 in base 36)
for (var i = 0, max = 11; i < b36.length; i += max ) {
chunk = b36.substr(i, max);
intChunk = parseInt(chunk, 36);
if (intChunk.toString(36) !== chunk) {
intChunk = parseInt(b36.substr(i, max - 1), 36);
i -= 1;
}
b16 += intChunk.toString(16)
}
console.log(hexString);
console.log(b36);
console.log(b16);
Update: You could also use a base 62 instead of 36 to compress more, but notice that JS supports up to base 36, so you need to implement that personal notation manually (I believe there are already some implementation around).