Maybe the issue is your washer does not extract water so wel
Combo; Your numbers are wet; ie not dried.
Here a typical load here is not 10-12lb load of clothes ; it is less. With the new LG washer it spins the clothes fairly dry; ie the dryer really needs little work.
If I washed your "You may dry 6 mens dress shirts in 30 minutes" case I am taking out the shirts after about say 5 to 15 minutes and placing them on hangers. At 15 minutes time they would be so crisp; ie real dumb since one now has to iron the stuff.
Things like dress shirts here are removed while not bone dry purposely; to reduce the chances of wrinkles. One just hangs them on hangers when they are about dry.
Maybe the issue is your washer does not extract water so well?
THUS Here RE "But in most cases of doing 6-10 loads per week in a gas dryer will make cost of purchase free after aprox 5 years and pay for itself many more times over its 15-30 year life span. "
does not apply. To wash that amount of clothes I will have to find a younger wife and have 6 kids; then it will make sense.
Here with any actual glass dial 240V watt hour meter in series; I have actual data. The actual KWHR's is like:
"Here with a typical wash load I do the electric dryer if it runs 1/2 hour and on half the time draws 5400 *.25= 1.35 KWHR. My actual measurements are all over the place; about 0.5 to 2; with 1 to 1.5 KWHR being typical as measured numbers with a dial KWHR meter in series. With the 1.35 KWHR number my drying cost is thus 1.35 * 14.5= 19.6 cents. "
I actually only save 10 cents per wash load if I switch to gas. To buy a gas dryer for me has no payback. My total cost savings is only 25 cents per week; 13 bucks per year. My house insurance will go up more than that amount. Thus If I win a free gas dryer and have free intall; it still costs me more since my fire insurance rises more than 13 bucks per year.
Thus *HERE* the venture has a negative rate of return and not done.
Here it really only makes sense for me if a start a giant family; then number of washes increases; the savings are then more than the insurance cost increase.
Real I was raised no to be wastefull ie not take on projects that have no returns.
The current dryer is already 35 years old dn well made; I really do not it buy into buying a new gas dryer for 500 bucks wtih install; that has a negative rate of return. You are free to fill landfills; here I this as ruining the planet. The old machine will last another 35 years. The motor, coil,belt are common; I have a brand new timer too. Maybe this is why so many are in financial troubles; they chase bad investments.
The dumb dryer here costs me about 1.35 Kwhr per load for *MY* average 2.5 loads a week. I burn about 15 KWHR per month with the dryer; *IF* it is raining and I do not use the clothes line. This costs me 2.18 dollars per month. This is actual measured consumption.
As a reference; that government kickbacked TV converter I have if left plugged it draws 9 watts 24/7 . In one month if left plugged in consumes 6.5 KWHR ie 9x24x30= 6.48 If I just unplug this converter box when not used I save as much as the gas dryer would; and I have no added insurance premium too.
Here about the largest electrical costs are ones Air conditioners one runs. In the summer one might have a 100 to 150 buck electrical bill; depending on how hot and how humid one wants to be inside.
If the electrical bill is say 120 dollars in July; one has 2.18 for the dryer ; the LED and CFL timed night lights are a few bucks too. The fridge here costs about 10 per month.
For me the 1992 Fridge costing 10 per month is the major thing slated to be replaced; since replacement makes cents

from a money energy standpoint.
Buying a gas dryer will never be done unless it makes sense to do so. ie why be wastefull?