Perhaps you have edited your post but I don't see anything about the dog getting only one hour of exercise a day. Assuming that's the part you edited I have to say how much I agree.
Your dog will not likely need an hour of training a day, probably that's way too much. But to excel in agility your dog will have to be conditioned. I think you need to examine how far you might want to go on both sides. Agility is very physically demanding and even advanced obedience is going to require a certain level of fitness for the jumping involved. It's a big, big, big committment for both of you. That's why my first Lab and I quit agility. The darn dog
just kept getting better and better at it and I did not have the time to devote to the conditioning and training she needed to keep competing.
My current Lab, three years old, needs more than an hour a day of off leash running simply to dispel his high level of energy.
More and more where I am agility classes are offered for fun with no intention of competition. Maybe this would suit you?
I do have to laugh a bit because you did not mention the Portuguese Water Dog. My sister's trainer breeds these dogs and also teaches obedience and agility. Her dogs are her best examples though she does not seriously compete, just trials now and then for fun.
I have never heard of the Portuguese Podengo. I googled them and it seems to me the smaller, smooth coated type rather resembles an Ibizan hound. Lovely looking dogs. Like the Ibizan the PP is a sighthound and a hunter. At the following link it says they enjoy agility.
When my girl and I were trialing in agility the dog most serious competitors had were either Border Collies or Jack Russels. My trainer used to say, "oh you poor people whose dogs are in the same height category as a BC or a Jack but aren't one of those breeds" LOL, her warped way to encourage us I guess.
But as said above many, many breeds enjoy and do well at either of the activites you mention. Many at both at the same time too. My trainer bred and trained Airedales. Other people in my classes had miniature Schnauzers, Labs, Keeshonds, Papillons, Shelties as well as the BC. The only dogs I remember doing very poorly at the agility was one Siberian (and just that particular dog, not the whole breed) and one poor little Basset who kept stepping on her ears when on the dog walk so it was not safe for her. She seemed to like it though.
I wonder if because the breed you have chosen is quite rare that the breeders you have contacted are very thoroughly scrutinizing potential buyers? My very brief bit of reading on them says they are primarily a hunting dog and perhaps the breeders want them to be used for the sport they were bred for? What did they tell you was wrong with the dog and the use you have in mind? Are you a first time dog owner? They do sound as if they need an experienced handler. Good luck, let us know how this turns out. It would be neat to see photos of a PP here, if you do get one.