If you want to live dangerously and go two different tickets plus airport change, Hipmunk says open jaw this:
Thurs, Sept. 18
IAH-DME on Singapore Air Singapore (SQ) 61
Marketed by Transaero (UN) 7061
Layover in Moscow for 9 hours and get to the next airport-
VKO-DYU UTair (UT) 801
in Coach on a UTair 321
Sat September 27-
KUL-DXB Emirates (EK) 347
in Coach on a Boeing 777-300 3-Class
10 hour layover in Dubai
DXB-IAH Emirates (EK) 211
in Coach on a Boeing 777-300 3-Class
for $1708 on Flight Hub ($1713 CheapoAir)
Then a one way ticket depart Thursday, Sept 25
DYU-SVX Ural (U6) 2954
in Coach on a Ural 320
10 hour layover in SVX
SVX-DUB Flydubai (FZ) 902
in Coach on a Flydubai 73H
DXB-KUL- Emirates (EK) 346
in Coach on a Boeing 777-300 3-Class
for $823 on Vayarama
Total $2531
This gets you into KUL at 3:05 on Friday with your KUL outbound at 7:30pm on Saturday, which is hopefully long enough for your needs. The choke point seems to be getting you out of DYU and pointed correctly eastward, with longer layovers likely no matter how much you pay.