There are ways to deal with Doomsday. The only really that GL can't deal with is Doomsday's Trait with SN MB. (Supernova) Even still he only has to time to do that once before his trait runs out. From there pushblocking or B3 MB will get him away, or if blocked leaves you at advantage.
If he activates his Trait and starts coming in to pressure, use MG MB to hold him back and cause damage until his trait runs out.
If he throws out a SN MB you can either dash and full combo punish, or an easier option, a delayed B3 MB for a full B3 combo punish. You will of course take damage with this option but it's only 9% vs your full combo punish damage. This will certainly make the Doomsday player no rely on SN MB.
As far as Sinestro, it's up in the air at the moment. Myself and
Pig Of The Hut believe it's 6-4 in favor of Sinestro, but
KT Smith suggests 5-5. I will be looking into this MU in depth very soon.
With Batman, it's very difficult for GL. Especially if the Batman player is aware and punishes the string gaps in GL's B1 strings leaving the GL player to pretty much rely on 223. Best thing you can do in this MU I've found so far is keeping Batman just within LM range by using pushblocking, throws, and limited OR and AOR zoning. It's winnable for GL but probably not in his advantage.