I was there in early spring a few years ago - in a similar situation to you - i.e. a non-birding holiday with a few grabbed moments...
The golf course at Port el Kantoui was my main haunt - good for migrants, but I guess that might not be the case at this time of year. Of the resident species, I had desert grey shrike, north african blue tit, and north african chaffinch, as well as sardinian warbler, and pallid swift.
I also had a wee trip to hergla salt pans - the water levels were too high for waders but I had slender billed gull and greater flamingo on the pans. In the farmland around I had stone curlew and great views of barbary partridge. It's easy and affordable to do this by taxi from PeK.
Finally, We signed up to one of the organise excursions in the hotel, that went south towards the desert (eg towards tatouine, chott el djeridd, Douz etc). It was very very frustrating as we spent so much time in the minibus but it did stop every now and again, and over the course of the trip I picked up trumpeter finch, hoopoe lark, mourning wheatear, desert wheatear, thekla and short-toed lark, house bunting, brown necked raven, and rather annoyingly, a heard only egyptian nightjar...