So I figured out how you succeed at Dreamworld.
Basically when you go do the isle of dreams, don't make a wish at the tree the first time, do a few passes through the isle again so you can find all of the pokémon and items available for the day.
Otherwise if you decided to send something to the entralink you can't search for more pokémon and items.
Start off by growing lots of simple berries like oran, pecha, cheri, persim, chesto, etc. They will produce multiple berries much faster for swapping or buying things in the catalogue.
I don't know for a fact, but I think upgrading your dreamhouse gives you a bigger garden so you can plant more berries.
When you are playing the icecream stacking game, you might not have noticed the icecream scoops continue to enlarge whilst you hold the mouse button, keep scooping until it's as big as the "bitesize" thing on the right side of the screen, you'll score more points.
Finally, when you visit other dream isles, if you don't have any dream pals yet you can always visit at least one random home. After visiting a home you can leave and visit another random home, and possibly all the homes befriended with that home.
Keep doing this for as long as you can for the hour and eventually you'll be able to trade lots of your lesser berries for stuff you don't have yet.
The EV berries, like kelpsy and pomeg in-fact do exist in the dream world, but they are very hard to come across by the looks of things. I've yet to see anyone share any of these berries, but I've seen people growing them.
And remember, when you visit dream isles, look for attractive players, ones that appear to be making an effort to expand their inventory as much as you are. If you find such a player, send a dreampal request so you can visit them reguarly.
Be warned though, since the feature just launched globally, a LOT of dream isles out there are completely empty, no berries planted to water, nothing on share shelves. Thankfully though, if you are allowed to visit a japanese dream isle, there's a much better chance of them having something to share.