Almaty to Urumqi by connecting train (via Altynkol and Khorgas)

Besides the direct train which runs twice a week (and, unfortunately, doesn't fit our planned schedule) what other options do we have to make the journey from Almaty to Urumqi by train/bus within a day/24 hours? We have a flight out of Urumqi on the 27th of October and would like to arrive the day (night) before to give us enough buffer.

I plan to split the journey into two parts, first, taking a Kazakh train from Almaty to the border at Khorgas and then a Chinese train from Khorgas (on the Chinese side it is called Huoerguosi) to Urumqi.

I have researched a few options but struggle to confirm their actual availability. First, there's Lonely Planet citing two daily connections between Almaty and Khorgas:

To get to the border at Khorgos, go to Almaty-I and either take daily train 702 at 8.01am (3483T, 3¾ hours) or train 394 at 11.51pm (2422T, 5¼ hours). A 15-minute bus transfer to the Khorgos border is included in the fare.

This information is cited on various travel forums but I couldn't find either train on www.railways.kz or any other online schedule so I assume this information is outdated.

A similar option (as pointed out by the Lonely Planet) is to take the train to Khorgas but then continue on a bus or taxi to Yining. How frequently do these busses run or how easy is it to get a taxi? How much would it cost and most importantly, how much time would we need to plan to make our way from the border to Yining, i.e. which onward train to Urumqi can we realistically aim for?

I can find multiple Chinese train connections from both Yining and Huoerguosi (Khorgas) to Urumqi (K544, K1338, K9710, K9718, K9790, T206, Y952), for example on www.trip.com.

On the Kazakh side, the trains I found for the route between Almaty and Altynkol on www.railways.kz and tutu.travel are 393T (00:50-7:34) which runs every second day and 886X/6986Х/7086X (8:36-15:11) which operates daily. Can someone confirm this information?

If these timings are accurate how can we bridge the gap between Altynkol and Khorgas/Yining? Is there transportation available and how much time do we need to plan for crossing the border? I didn't find any information about potential border closures but maybe someone can share their experience crossing at Khorgas on a weekend.

Lastly, for further research, could anyone confirm the Kazakh and Chinese names for Khorgas/Khorgos/Korgas/Qorǵas?

This question covers the same route but I am explicitly asking for a different connection.

Update I found the bus from Almaty to Urumqi on Sayran's webpage. There's a daily connection at 7:10 (if I click on the details it says 7:00). There's not as much information as for other connections but it appears as the bus stops at Khorgos (I don't know which side of the border though, and whether it's possible to get out and continue by train from there). It's a 24 hours ride for 16000 tenge.

There's also a connection from Almaty to Zharkent (2000 tenge) every other day at 9:20 (again the detailed information mentions 9 am sharp):

[...] Zharkent, from where a bus to China leaves twice a day, while minibuses leave when full (average wait 2-3 hours, less in weekend).

There's also a report about someone making the trip from Almaty to Yining by bus.

Source