BTW the judicious use of spurs will do more to help a horse collect than the use of draw reins. :)
You and Kayty had some REALLY good points- Spurs are a wonderful tool to get horses to engage their back and and lift their barrel. I also loved hearing you say "back to front"- so many people forget this important part, and draw reins absolutely prevent people from following this basic fundamental. My instructor lives and breathes "back to front", which has absolutely transformed my horse for the better. In the case of the horse I used draw reins on, it was an OTTB who would try to go over backwards, they were never used to get his nose to his chest, EVER. They helped him realize that he could find comfort and balance with his nose about 30 degrees in front of the vertical, my goal was not even to get him AT the vertical at that time. They were used for about 10 minutes 4 days in a row. The other important piece that Kayty and Elana touched on was "back to front"- can you get your horse to lengthen his stride from behind? Truly lengthening his stride and asking him to reach further up underneath him is actually quite hard for lots of horses if they aren't muscles they are used to using (*also, when I give a lesson and ask someone to lengthen their stride, they kick and ask the horses to go faster, this is wrong!) In a western horse especially, they can get tight in the hamstring if they are asked to go slow all the time. I have a retired WP horse, and asking him to get long and low and reach up under him with his barrel swinging through is HARD.
I would work on stride lengthening, and like Elana said, hills and cavaletti. It is possible that what you are asking your horse to do at this point is more than he thinks he can; true collection takes YEARS of correct conditioning- you don't see 5 year old horses schooling grand prix for a reason. One exercise I have my students to is to get their horse in a relaxed walk, where the horse can really swing their head back and forth. By letting them do that, you can really engage the topline. The nuchal ligament goes from the poll to the tail, and works like a pulley system- when it is relaxed the withers can pull forward and the spinal processes can open up, therefore supporting your weight more efficiently than pulling a horse down in frame or on the forehand. When the inside hind comes forward, gently squeeze the barrel and ask them to take a larger step. Don't worry about your hands or your horses head set, your goal is to get them to open up their back end. Your hip will dip just slightly as the leg starts to swing forward- by cueing just as the leg leaves the ground, you can control how far they step forward. SO many people just squeeze randomly to extend a gait, but as a rider you need to be aware of the footfalls so you can control and direct where your horses places each of its legs; the head has NOTHING to do with this right now! As your horse starts to find balance from behind, collection will become easier. Doing this slow, and in a relaxed manner, can be REALLY hard! Whenever working new muscles in a horse, keep a realistic goal- our little WP horse can hold 2-3 good strides at a time- he can't go for 15 minutes around the whole arena. Setting realistic goals is important. A muscles needs a break after 20 minutes, so changing up your exercises will also help you from exhausting a muscle and ending on a "bad" note- hope this helps!