Do you have a 'reel' mower, is that the same as hover mower? Your line trimmer should have no problems getting the heft out of your lawn, once in a while, your grass will deal with it just fine. Try to not lop off more than 1/3, if not short enough for your reel mower, wait a week and lop off another 1/3.
What I am fairly sure you are doing is allowing your line to be TOO LONG. Pull both lines up above the middle of your trimmer head, cut them off about 5". Then to perfect the length of the lines for the sharpest most accurate cutting with a line trimmer...turn the trimmer upside down and touch the spinning line tips to concrete or a boulder. You'll hear the rpms go UP and then you will know the lines are perfect to cut grasses, weeds and take care of the motor of your trimmer. To squash down the grass like crop circles tells me your lines are far too long, tough on the motor of your trimmer and the speed at the end of the lines is so slow they are unable to cut anything.
Is your trimmer gas or electric? Do you have a blower? The only equipment I will use is gas powered. Gas with NO ethanol. Proper mix of the best 2 cycle oil you can find. Keep your filters clean, changed out to keep dirt out of the engine and your trimmer, blower, mowers will last forever. Electric is just too lame. sorry. Gas is far more powerful and easier to use. Get rid of the bump and go head, get a fixed head, proper line and also get rid of the shield so that you are able to see exactly what you are doing. Always wear safety glasses and be aware of your surroundings...and where you are 'tossing' rocks, debris! That shield in my opinion is worthless, giving the user the sense they don't have to be aware of the 'tossing'...a single little pebble becomes a bullet, no mistake!
When I have to mow too long grass or too wet grass, I use my blower to fruff up the grass, blow moisture and weight off. I'll do this prior to cutting and after and then a light touch up. Bag clippings...mulching mowers aren't yet true mulching mowers and there is always a great place to use clippings (compost)?
Talk to the lawn equipment service men...they can be your best friends.
MOW NO SHORTER THAN 3"!! Unless you are a golf course, a home lawn needs to be 3" (cool season grasses) or you will have weeds, wimpy grasses. Keep the blades of your mower super super sharp. Otherwise it will cause ratty ends and a grayish look to your lawn. Aerate your lawn once per year pulling out plugs and leaving them on your lawn. Water DEEPLY (4=6") and allow to dry out before watering again. When your footprints on the lawn stay down, that is the perfect sign to water again. Otherwise use a shovel and look at your soil profile.
And mowing once per week is minimum, twice is cool (always at 3" no shorter). Try not to allow your grass to grow too long, pretty stressful on both you and your lawn. What are you using for fertilizer? Believe it or not the expensive organic (extended release inherent) stuff is BEST. Not the fast, commercial fertilizer by Scott's or Ortho...Try something like Dr. Earth's lawn fertilizer. I was (as a veteran of lawncare) blown away with the results. You don't have to use it more than twice maybe 3 times per year versus the absolute must of 4X per year. Watch the formulation for different seasons! You should never have to use any other chemicals ever with this methodology...