Hardy cartridge

I own many ADC carts and have NEVER broken or damaged one in 40+ years. Truly, if you’re really that clumsy, NO cartridge is safe in your hands! Not a Grado, AT, Shure, Ortofon, or heaven forbid an MC cartridge! 

I have the ADC Point 4 with nude conical 0.4 mil stylus, the 660, 770, 10E MKII, 220XE, 10E MKIV, 25, 26, Q36, XLM, XLM MKII and MKIII, NAD 9200/9300, VLM, ZLM MKIII, QLM 36/34/32/30, Astrion, TRX-2, PSX-30/40. Never, ever, damaged a stylus. 
I have 108 cartridges, 150+ styli. I change headshells and styli 2-3 times per day. Never damaged a stylus or cartridge. 
Before you buy another cartridge or stylus, learn how to handle what you have!

Getting memories of old automatic turntables that automatically cued the tonearm to the beginning, automatically reset at the end, and allowed stacking to automatically feed next record. IIRC it was a GE Trimline record player. The amount of vinyl abuse back then would make us cringe today.
Apologies a bit off topic.

@fstein
What you need is a “cueing lever” that lowers and raises the tonearm.  They come in various sizes/heights so check if meets your needs.

The disaster actually has nothing to do with cuing...it occurs with stylus cleaning, using all of the generally approved methods such as blutac, gel, camelhair or carbon fibre stylus brushbrush (back to front), ultasonic stylus cleaner...tried them all, sooner or later ->tears.

Add a cuing device to your TT. DJ carts were designed for abuse...and sound like it too.

Option 2. Place the cart on the record and then start the TT afterward.

@fstein, You have a very light tonearm. The specs just give you an idea if you are reasonably close. You have to use a test record with vertical and horizontal resonance tracks. These are usually very easy to use. First you get lateral resonance right by adding weight until you get the resonance down to 8-10 Hz. If it is already there you do not have to add anything. If it is lower you have a problem because removing weight is much harder. Usually, I go to lighter screws, either shorter or aluminum. Once you have the horizontal sorted you look at the vertical. Vertical resonance is affected by tracking force, add more and the suspension gets stiffer and the resonance frequency goes up. Add less and stiffness drops to a point and resonance goes down. I usually start at the highest recommended tracking force and work my way down. I just set up a Soundsmith Voice. Once the horizontal resonance was down to 8 Hz the vertical was up at 12-14 Hz, too darn high. Dropping the VTF by 0.2 grams brought it down to 10-12 hz which is where I left it. VTF is a pleasing 1.5 grams. It only took me 20 minutes.

IMHO this is more important than VTA. This will determine how well your tonearm follows warps, how well the cartridge tracks and how detailed your bass is.