Unfortunately, although Shimano makes some of the better brake calipers that you can use, the probable "problem" was not with your original brake calipers, per se ...
Just my recommendation, and it may NOT resolve the issue, but the first thing you should do is to LUBE the brake cables (and, essentially their housings) DESPITE the general belief to the contrary with Shimano cable housing ... at this point, just wipe the cables with a thin coat of VASELINE ... no excess.
BTW. CHECK HOW THE HOUSING IS ROUTED ... disconnect the cable from the caliper, push it forward a few inches (with the lever partially "closed" to expose the end of the cable), grab BOTH ends & pull the cable back-and-forth to ensure that there isn't any binding.
AND, CHECK THE ADJUSTMENT (is the quick release open?) ...
There are differences of opinion as to WHEN the brake pads should engage the rim ... I prefer that engagement occurs when the brake lever has moved about 20% (?) of the way to the bar AND maximum "lock-down" is probably at 50% ... this allows ME to modulate the braking better. I know one shop that sets up the pads so that the pads engage when you move the levers about 10% of the way to the bar & "lock-down" is probably at 30%!
When the quick-release is OPEN, the inner shifting blade is almost touching the handlebar the way my brakes & levers are adjusted.
Campagnolo cables & housing are the "better" than Shimano's ... basically, pre-lubed (but, not cheap).
The LAST option is to change the pads ... some pads are made with "harder" rubber than others
NEVER RETURN TO THAT LBS FOR PARTS OR SERVICE other than a free resolution of the existing "problem" -- that shop's concern is seling you parts at a premium (over mail order) ... otherwise, I presume you spent $100+ for the pleasure of NOTHING.
If you were dealing with brake calipers on a 20+ year old bike, the situation might be the calipers (because of the length/reach); but, honestly, I have all kinds of brake calipers on my various bikes ... and when properly adjusted, I did not experience the problem you suggest BUT when not properly adjusted OR before the housing was lubed, the situation could probably be described as being similar.