Ah the joys of single pilot flying.
Funny that it is usually single controller operation at the other end also.
When ATC are called while busy with something else eg on the phone coordinating they will tell the pilot to standby - perfectly acceptable.
When the pilot is busy he should likewise tell ATC to standby thus indicating that they are busy. This is also perfectly acceptable and uses less R/T than a series of half-heard or incorrectly read back clearances.
The initial clearance would have been safe and the following "re-clearance" would simply expedite the situation for you or another aircraft.
Regards,
DFC