Scott---
Marv hit the nail on the head when he wrote in his post above "or screw extensions onto the ones you have."
Assuming you have what are known as pop up impact heads - like this one:
But even if it's a different brand/model....they all screw onto a threaded nipple, and that's where we go to address your issue.
Most sprinkler heads have either a 1/2" or a 3/4" threaded inlet at the bottom of the body, where it screws onto a nipple (as stated above).
Smaller heads have the 1/2"....larger ones have the 3/4". If you are running a head that rotates and is designed for a larger radius - such as a lawn area - chances are they have a 3/4" inlet.
If your system was constructed with each head on a section of flex or funny pipe - you can dig around each head to loosen, and raise the head up as needed without unscrewing or changing anything else.
If the heads are not on a section of flex or funny pipe, the easiest way to raise them is to use an "extension nipple":
They are "poly", which is the nice soft stuff that is easy to screw in - and more forgiving than(for example) the gray colored schedule 80 stuff that some nipples come as.
That one pictured is a 3/4" - and they also come in a 1/2". You will know which ones you need after you unscrew your head and look at the inlet at the bottom.
These nipples are different than 'normal' nipples because they have a male on one end and a female on the other - so when you unscrew your head....you have one end that is male and one that is female....and this nipple goes back in between the two....and just like that....your head sits higher than it was. Note also the nipples are segmented so you can cut to desired height.
I have had situation where I put these in at full length and also where I made the decision to cut some off. You will get the hang of it after the first couple heads are done.
Based on your post, this would be the easiest and most efficient path to take to raise up your heads. Your goal obviously is to raise them as high as possible without being so high that the mower blade will hit them.
Make sure you pack the soil down real good around each head as needed.
BTW....I like using those concrete donuts sometimes in turf area around my heads so I have a nice spacer to protect the heads when I weed whack around them, which should be done routinely to keep the grass from covering them up.
Some folks like the grass covering them to hide them but the German heritage in me goes with the more practical approach.
Plus the most popular turf species in these parts is St Augustine which is a creeper and has very strong stolons which are capable fo restricting pop ups from popping up!
So - this is a job that you can do just a head at a time....or two or ten - or all 30 - as you desire. Take your time.....if you are careful when you unscrew each head you won't have a bunch of dirt fall back into the opening. If that happens you may need to blow that opening out before re-installing the head. Do this by attaching the extension nipple alone and briefly running that zone...then let the water drain down good....then proceeding.
All of this is common sense so a person like you shouldn't have any problems but if you do or I can help with questions please let me know.
You should be able to buy these extension nipples at your local box store or online or at the local Site One store if there's one nearby.
Good luck!