The GOP knows that they do not really have a chance of winning this fall if people actually go out and vote. Their best chance, because of how despised their Presidental canidate is to ensure that only supportes of Trump actually go out and vote, with the hope that is enough.
Yes, the GOP wants to suppress voting, particularly early voting. In general, those who vote early are well-educated on the issues and have thought out their choices. At the moment, very few people are ready to actually cast a vote for Trump. His followers will wait to the last minute, wanting to cash in on all the excitement along the way. His questioning supporters want to wait and see before voting. He has nothing to win from early voting.
I don't think that the GOP calling for limited early voting hours has anything to do with suppressing voting. After all, the hours would be limited for both sides. In general, if people want to vote, they will make it a priority. If they don't care, then having a few extra hours isn't going to make a difference.
The more that voting is extended and allowed out of hours, the easier it is for voting irregularities and fraud. A person doesn't have to appear to fill out a ballot. Rather, they can ask for a bunch of ballots for people who are dead or not able to vote, and vote in absentia in the name of those people. The GOP just wants to keep things honest.