The 124/2.6 is a torque shy engine in a fairly heavy body. I believe your car normally starts in second gear, and if you floor the throttle it will downshift to first, but this will take a second or two. The chirp you hear may actually be the downshift to FIRST gear.
If you move the gear selector to "L" it will start in first gear. Try this and see if it makes a difference.
The behavior you report may actually be normal. The second gear start and slow throttle tip-in is characteristic of Mercs to make them smooth, but it can also make them seem slow when you are trying to make a quick start from a dead stop.
A slow shift to first gear on a WOT start may be possible to correct with adjustment of the kickdown linkage, but I'm can't give you any guidance on this as my 201/2.6 has a manual transmission.