That way of installing the impeller is not really necessary, because you can use a sticky marine grease like Evinrude triple guard to hold the o ring in the impeller housing slot and it will not move out of place when you have to twist the housing to get the impeller on. I like to lube up the new impeller with a mix of water and Dawn dish soap. I've been doing them this way for 15 years with no problems.
If that housing distorted and the metal cage shifted, its likely that you did not have enough water flow to the impeller. If on land your muffs may not be sealing well enough, or the water tube gaskets inside the drive may be bleeding off water pressure and starving the impeller. Way to check:
before you install new impeller, hook up muffs. The impeller mount has 2 openings, one is the inlet, one is the outlet. Right side is the water inlet, left side is the outlet which sends water through the transom. So....
Hold the muffs tight to the lower unit have someone turn on the water, water should spurt out of the right hand side, if not, you either have bad water tube gaskets (requires splitting the upper and lower to replace) or a blockage in the water intake area. If OK then good. Now, you want to back flush your hose from the stat housing to the transom mount. Have your helper stick a garden hose in that hose after disconnecting it at the stat housing and turn on the water. Water should spurt out the left side. If not, then there could be a blockage in the P/S cooler which is in line with the hose from the stat housing to the transom mount.
After I install a Cobra impeller I always run it on the water hose with the cover off, so I can see if the bleed hole is open and spraying water and and to make sure there are no leaks around the impeller housing.
As long as your raw water flow is good, no obstructions, these impellers last easily 3-4 seasons. Even then when I take them out they are hardly worn.
BTW I always use OE for the impellers, and driveshaft bellows. Do not use off brand aftermarket if you can't get OE I would use Sierra, but you can't mix n match, ie use a Sierra housing with a Sierra impeller not OMC + Sierra because they may not work well together.
I found over the years I've had this boat I have found that the OMC Cobra cooling system design is pretty trouble free, the only issues I have had was due to my salt water use where I had to replace manifolds more often and I had barnacles growing in the lower unit water intakes, I wound up splitting the drive taking out the screen and leaving it out for good. This way I can rod out the water intake holes with the boat on the mooring.
If you had no oil in your upper gear housing, remove the 4 bolts holding the top cap on and take a look at those poor upper gears. My guess is you will be buying a remanufactured one. The drive when full takes approx 2 qts of gear oil.