One thing I have learned over my years when selecting a shipping company, I noticed your top criteria was “cheap”. While I don’t have specific recommendation, this is just a good rule of thumb or guide.
3 KINDS OF SERVICE - GOOD,FAST,CHEAP
YOU CAN PICK ANY TWO
GOOD & CHEAP WON’T BE FAST
GOOD & FAST WON’T BE CHEAP
FAST & CHEAP WON’T BE GOOD