Should my 1099G total for Unemployment include the extra $600 weekly payment from the CARES Act? I understood this was non-taxable per the CARES Act. Is this correct?

You misunderstood,  That extra $600 per week is taxable income.   You have to enter all of the amounts you received. 

UNEMPLOYMENT COMPENSATION

Unemployment compensation is taxable on your federal return. 

You will have to enter a 1099G that is issued by your state.

Some states will mail out the 1099G.  Or you might need to go to your state’s unemployment website and use the password, etc. that you have been using to certify for weekly benefits to get your 1099G from the state’s site.

Enter your 1099G in Federal>Wages & Income>Unemployment

Go through the screens very carefully, making sure  to enter any federal/state tax you had withheld from the unemployment.

https://ttlc.intuit.com/community/entering-importing/help/where-do-i-report-a-1099-g-for-unemployment-or-paid-family-leave/00/26530

STATES THAT TAX UNEMPLOYMENT BENEFITS

AZ, AR, CO, CT, DE, DC, GA, HI, ID, IL, IN, IA, KS, KY, LA, MA, ME, MD, MI, MN, MS, MO, NB, NM, NY,NC, ND, OH, OK, OR, RI, SC, UT, VT, WV, WI

STATES THAT DO NOT  TAX UNEMPLOYMENT BENEFITS on the state return

AK, CA, FL, MT, NH, NJ, NV ,PA, SD, TN, TX, VA, WA, WY

https://ttlc.intuit.com/community/personal-income-taxes/help/how-does-receiving-unemployment-affect-my-taxes/00/1756152