I was at Kinabalu NP in early April this year, and stayed just outside the entrance gate at Mountain Resort (25 R/night shared room), whih is just a few hundred meters further along the road, comming from KK. There is a very good and cheap restaurant across the road from the entrance, with a guesthouse attached, so absolutely no need to stay in the expensive hotels inside the park.
I walked/hiked/birded the trails for 4½ days, doing the summit trail up to 2600 m once, and alos visited Kundasang a 10 minutes drive further downhill from the NP entrance (buses/huítchhiking) to see Bornean Ibon as well as Dusky Munia and Blue-breasted Quail.
There is no need in my mind to rush up to Bukit Ular every morning, as the trails lower down are also very birdy, and wind their way uphill anyway, and I found birds like Whitehead's Broadbill and Trogon on Bukit Ular in the afternoon as well. But then again, I was blessed with mostly dry weather during my stay, with a few afternoon thundershowers, that could be waited out in one of the many shelters.
I think it would probably be a good thing to try out different trails at different times of the day, to get a good range of birds.
Jens