Looks Like Colin and I are equally excited about meeting you here on the forum. It is a real honor to have you here.
I did a bit of investigating last night and this is what I found. These references were found in my Corps of Engineer book which I have listed on this site.
The 343rd was a General Service Engineering Regiment, who indeed came into action with the Sicily Invasion. They even worked and fought in the very same places that my father's unit, the 540th did. That was a pleasant surprise.
Behind II Corps, the 20th Engineer Combat Regiment on Highway 113 and the 343rd Engineer General Service Regiment on Highway 120 shared road maintenance responsibility within the army area.
The 20th Engineers improved 18 bypasses on Highway 113 between Palermo and Cape Orlando, and the 343rd did similar work on 21 bypasses on roads from Cape Orlando to Messina and Randazzo.
The 540th CE Reg (less on bn) worked briefly at Palermo, then moved on to operate the beaches at Termini Imerese. The 343rd Reg whose responsibility for Palermo was also brief, replaced the 540th on July 30, 1943.
The following is in regards to the invasion of the Italian mainland:
The 3rd, 34th, 36th, 45th Inf Div's along with the 82nd Airborne and 1st Armored Division were the main invasion forces and of course had their own permanently attached engineer units. A navy beachmaster was to maintain communication with all the ships and control all operational landings. A port HQ consisting of two Transportation Corps port battalions, was to coordinate all unloading into small craft offshore, but the pivot of beach supply operations was the 531st Eng Shore Reg and the 540th Engs, the former assuming responsibility during the assault phase. The 531st, a component of the 1st Engineer Special Brigade for the invasion, replaced the 343rd Engs, which was trained in beach support operations but had neither the experience nor the equipment to carry out this function.
This is in relation to the Volturno River crossing:
From the time the troops crossed the lower Volturno at Capua and Caiazzo to the time they crossed the upper Volturno and Colli, they were extremely short on bridging material. They had to resort to low-level bridges and mainly used materials that were scrounged up from the local country-side. Flash floods played havoc with most of the bridges and many were completely wiped out.
The one bridge sturdy enough to resist the torrent was a semi-permanent structure that the 343rd built at Capua between Oct 16 & Nov 9th. This pile bridge was a major link in the 5th Army lifeline for a 6 month period!
That bridge was 332 ft high, 370 feet long, and was classified as a two-way Class 40, one-way Class 70 bridge. In the first 24 hour period after the bridge opened for traffic, 10,000 vehicles crossed. During the campaign, 1 million! Way to go boys!!! 
During the June and July drive to Arno, much of the 5th Army forces were preparing for Operation Anvil (the Invasion of Southern France). The non-divisional engineer units that split away from 5th Army control included the 36th, 540th & 48th CE Regiments and the 343rd & 344th Engineer General Service Regiments.
Here's a reference to Aix, France in August of 1944:
The 343rd Engineers restored service to Aix in ten days by a strategem that saved days in repairing a 104 foot gap in a rail bridge. In the area the regiment found a German 270-mm railway gun. They hauled it to the site, stripped the gun and the rail trucks from the traverse base of the piece and attaching a ten-foot steel extension, launched the platform as the stringers for the new span across the void in Bailey fashion. The Aix bridge work was completed on August 29th.
At the same time they were restoring a bridge at Meyrargues over rising river levels. After closing a 107-foot gap with the first Bailey Railroad bridge in France, a quadruple-single span with a deck thirty-eight feet above the water's surface, which opened to traffic on September 18th.
The 343rd was assigned the job of opening the Marseille-to-Lyon route, and began work on the Livron Bridge on September 7. Before the war a masonry-arch bridge has stood and had carried a single track across a muddy-shallow Drome. Now all that was left was a pile of masonry with a 310 foot gap. 
The 343rd placed steel I-beam stringers and by Sept 20 the bridge was open to rail traffic 5 days ahead of schedule. 
This performance along with the units previous actions in the southern Rhone valley, earned them a commendation from Lt Gen Patch.
After October 30, 7th Army Engineers divided the responsibility for rail rehabilitation. The 1st Military Railway Service supervised the construction of forty-two rail bridges and the repair of nine between Marseilles and Dijon by early 1945. The work continued and was performed by the 40th, 94th, 343rd, 344th, and 540th Engineer Regiments and the 1051st Engineer Port Construction and Repair Group.
