Which IR receiver (exact part number) are you using?
There's nothing you can do in software to influence pulse/space detection, this is performed inside the IR receiver.
Basically there are 2 key parameters for choosing an IR receiver, one is the carrier frequency of the IR signal (usually 36-40kHz), the other is the remote protocol a receiver has been optimized for and/or how well it can deal with external IR interference (eg sun shining directly on the receiver, nearby CCFL lamps etc).
Usually using a 38kHz (which is used eg for NEC proto)l receiver will work fine, 36kHz (used eg for rc-5 and rc-6) and 40kHz (eg sony) are near enough to work fine.
As for protocol optimization have a look at the last page of this document on the Vishay website: dataform.pdf - more detailled info are in the specific datasheets of the receivers.
AGC1 is the most universal AGC implementation, AGC4 (which is optimized for eg NEC and RC5/6) doesn't work well with a bunch of protocols.
So, my recommendation would be to try a TSOP34138 (1 is the AGC version, 38 the frequency). TSOP34438 (AGC4) could be problematic.
Some IR protocols have a rather large pulse/space at the beginning (eg NEC starts with a ~9000 pulse and ~4500 space) and you'll also see a large space (or a timeout) between button repeats. But the other pulse/space values within an IR message are usually in the 400-2000 range.
I searched a bit and the original Xbox remote indeed seems to use a non-standard protocol. So in-kernel decoding won't work, but you could be able to create a lircd.conf with irrecord (you might have to use irrecord raw mode if normal mode doesn't work) - but first you have to sort out the IR reception (pulse/space) issues.
As for the old lirc_xbox driver: well, that never made it into the official Linux kernel, OpenELEC/LibreELEC included it as long as possible (it needed a bit of tweaking now and then, but not too dramatic), but it's time had ended and we had to drop it. All IR receiver drivers in the kernel got moved to a new code base (which allows IR decoding in the kernel) and the old code lirc_xbox was built around got dropped.
so long,
Hias