Let me start by saying that it would've been better had you began to do this a month ago or so ago, but it's not the end of the world. If you know what you are doing, you should be fine.
Feeding dry beet pulp will work just as well as feeding it wet... you are on the right track by feeding him more beet pulp. Also, I'd start giving him free choice grass hay too. And I'd cut back on the corn in the ration a little bit & replace the corn that you remove with an equal part of whole oats. The Oats will increase the protein somewhat, but with the extra beet pulp & grass hay, it probably will balance itself out... but, keep that in mind.
Weigh him every week, or more often, if you can, & monitor the progress. If possible, start slowly increasing the grain leading up to the show.
A few other things that you can do...
Hauling him will shrink him. If you don't mind driving him around, you can help to keep the weight off a calf by hauling him around. And obviously, hauling him before weigh in will shrink him.
Withholding some water on weigh in day, until after the weigh in, will make him weigh less. But, if you have to weigh back in to make a certain weight after the show, make sure you stay within the limits. Common sense & preferably some experience, is needed when doing this.
Exercise... Walking him a lot, will help. Turning him out at night into a big open pasture will help. Turning him in with a group of heifers/cows coming into heat will help. Actually, anything that keeps him moving will help.