What you are describing is entirely normal for CAS radios. They are complete garbage, from top to bottom and on all sides. It's regrettable you didn't do a search on this forum before buying one. But now you know to avoid them in the future.
I have a Retrosound radio in my '66 fastback that sounds okay, works as it should, plays MP3s, and fits the stock hole. You might see what they offer for '68s.
Since (I think) the '68 radio opening is bigger than than '65-'66, you may have other, even better options. Posting here was a good move - someone will know, and hopefully chime in.
PS - someone may chime in saying that "the latest generation of CAS radios are okay, they have fixed all the problems." Don't believe them. I have been hearing that same BS for 20 years.
"When a woman is a really good driver, she is just about perfect."
- Raymond Chandler
'66 GT Fastback show car, nightmist blue, warmed up original 289 & T-5Z, 3.80 trac-loc, AC, PS, pony interior, Retrosound, rally pac
'66 Coupe driver, Bullitt green, 302HO w/ 351W heads, roller rockers, Holley 600, T-5Z, 3.55 trac-loc, collapsible column, tank armor, disk brakes, shoulder belts
'11 BMW 335i X-drive, 6 speed manual, all the bells and whistles