Would changing from the stock shocks on a 1200 Sportster to the Progressive 412 shocks make a noticeable difference in the ride? I wouldn't mind spending the money if there was a difference one could feel!

 

They did help little on my 48. I got the 12" shocks to give it a bit more travel and it did help a bit but not much. I hear the 444 series are the way to go if u get Progressives but are quite a bit more than the 412's.

 

I here a lot of guys have put road king and or street glide shocks on their sportys with great results

 

I put 12.5 inch heavy duty 412's on my bike. After they got broke in I am enjoying a nice plush ride with lots of travel. They shock they replaced were 10.5 inch 412's with little travel. I was impressed with how well they worked considering that there was only an inch or so of travel. I have not ridden the bike with stock shocks but I hear they are harsh.

BTW I noticed a huge improvement in handling after installing the longer shocks. It now loves to corner.

 

As an option, perhaps look at DK's new shocks that they tested, Bitubo or Pro series. I run SG air/oil shocks and according to Kevin, the ride is significantly better with the Bitubo...and the SG shocks are pretty darn good. I believe the Bitubo is better mainly because it has more travel and it's adjustable...so compare the travel and adjustability of the 412 and 444 with the one's from DK.
I special ordered the Bitubo in chrome and waiting for shipment....so can't give you a butt assessment.

http://dkcustomproducts.com/Rear-Shocks_c651.htm

 

There are countless threads in here on shocks! It is a frequent subject, not least because our bikes come on such poor quality stock ones. Before you buy are you clear what you want to achieve? Progressive Suspension offer five different models of shocks that will fit your Sporty, of which the 412 is the cheapest.

 

I put the 412's on my 07 1200C and I'm happy enough. I went taller and got the 13" if memory serves...

 

I also have the 412's. I bought the 13 inch length. The ride is much better (don't have that punch into my spine over hard bumps) but I don't know whether it's due to the shock, the extra length or a little of both.

 

I faced the same issue you did on my '09 Sportster. The Progressive 412-4068 have improved the ride greatly with both more travel and no more bottoming. I also did not care to break the bank on new shocks. After much research I found you could improve ride quite a bit for $200 to $250.
Got them on a well known internet seller the same name as a large S. American river. You will find several sizes there if you search for: " Progressive Suspension 412-4068C Chrome 12" Standard Replacement Rear Suspension Shock" You can select a black model 412-4068B as well.

First, I would not go any more than 1" longer than your stock shocks. This would likely mess with the front fork rake angle and steering. Some have gone longer and then found they were too long and too stiff, handles quirky, and ended up going to 12". I researched several brands and models of shocks and chose Progressive 412-4068. This model is a 12" shock, had increased travel. . . but also had an increased spring rate of 90/130 verses stock 75/115 (in spite of being listed as a "Standard Duty" spring). There also is a Progressive 412-4069 in a 12" size that has a 115/155 spring rate. But you do not state your size and weight and this shock is usually a bit too firm for most folks.

I found the Progressive 412-4068 to be just right and adjust the preload accordingly depending on the load I am carrying which can vary from 50 to 150 extra pounds. Remember, the new shocks will wear in and if you start at the lowest preload setting or ride 2 up or with gear, you will need to crank them up after a few hundred miles.

Pictures below of these just after I installed them.

 

Hands down, best upgrade on my bike...well, maybe tied with the seat upgrade. I went from stock 11.5" which were AWFUL to Prog 412 12". If I knew they would have improved my ride as much as they did, I would've put them on the same week I got the bike, instead of waiting almost a year.

If you do get them, I'd recommend adjusting the preload to the middle (position 3) spot, and they experiment from there. I started out with no preload (softest setting) and I thought the shocks were junk, until I figured that out.