First of all, your Culligan rep is an idiot. Is there anyone else locally you can deal with, or is there a more knowledgeable rep available? 34 ppm iron is incredibly high and REQUIRES a separate iron-removal unit place BEFORE the softener - Always, without exception, before the softener. If there is no-one else to deal with locally, find out what, specifically, the media in the Culligan fitler is and inform your rep that if you install it, you will install it in the correct location upstream from the softener. There are many possibilities for iron removal. Your iron is so high that it may require a combination approach to effectively remove all of the iron. Each approach has strengths and weaknesses and each of them will require some attention on your part. Since water has so many variables that affect treatment, a more comprehensive water test is going to be vital before we can get terribly detailed. In addition to the information you have already provided, we should know: manganese, sulfur (and if it is present, in what form), nitrates, alkalinity. For a little light reading while you await test results, look up the following possibilities for iron removal: 1) Pyrolox/Terminox (typically require nothing else, but in your case will likely require pre-oxidation in the form of air injection), 2) Birm (absolutely will require additional pre-oxidation, 3) Air injection followed by filtration media (typically not very consistant at higher iron concentrations) 4) ozone (expensive) 5) hydrogen peroxide (effective and relatively inexpensive, but does require that you purchase and handle the chemical) 6) greensand (effective but requires you to handle potassium permanganate which dyes organics and lovely shade of purple-black). You will want to look up these treatment methods to see which you may be able to handle. Frankly, any of them would be better than your current setup. I tend to lean toward the first option I listed for ease of use, but we are talking about your home, not mine so you will want to familiarize yourself with the possibilities.

Rebuild the head

"The problem may be as simple as a plugged outlet manifold" In THIS instance the Culligan service tech was on-site and diagnosed the problem as a resin problem and priced the repair which was replacing the resin. If the OP agrees to the repair (regardless of price negotiations) and that is NOT the problem then the OP should refuse to pay. "Adding a carbon tank before the softener to remove the chlorine will certainly extend the life of the resin..." It will, but at the risk of removing the anti-bacterials from ALL the water in the house. A subject of great debate among water treatment and (public) health professionals. Re-bedding a softener at 8, 10, or 15 years is a maintenance cost far offset by the reduced cost of premature plumbing, fixture, appliance repair or replacement, and the money saved by using far less detergent and clothes lasting longer afforded by a water softener. "... and give your family much higher quality water" A completely subjective opinion and also a subject of great debate.

Be good to know the size of your softener. Sounds like a salt bridge at the bottom of the tank. When the salt bridges (hardens) the water can't make brine, you don't use salt, and you don't get soft water. Remove as much salt as you can by HAND and throw it away. NO POINTY TOOLS or you poke a hole in the brine tank. BE CAREFUL AROUND THE FLOAT AND BRINE PICKUP. Whatever solidified salt is left can be dissolved with hot TAP water from the faucet. Remove it all. Dissolve any and all salt at the bottom of the brine tank and around the float and brine pickup. When the brine tank is all clean add a bag of salt (note the level of the salt in the tank) and 5 gallons of water. Wait two hours and do a manual regeneration. After that regeneration, with no water use, do a second manual regeneration after following the next paragraph directions... After the first regeneration the softener should have put water back into the brine tank. Add a couple gallons of water to the brine tank and wait two hours. After the two hours do the second manual regeneration. The salt level should have dropped and the correct amount of water will be in the brine tank and you should have soft water. Remember, the water heater is full of hard water so you'll have to use that up. Correct salt level in the brine tank should be 1/3 to half full or covering the water and check weekly. Fill it up with a lot of salt and you have bridging problems. Let us know how that works out.