SFO Local Controller reported a situation where a towing air carrier aircraft did not tow fast enough across the runway causing an arrival aircraft to go around.

Narrative

Runway 1R was closed because last week's storm knocked out all of the 80+ lights and signs associated with the Runway exits; which still has about [many] days to go for repairs. There is also a long term closure of Taxiway Zulu at Taxiway Charlie that creates a need for all inbound and outbound maintenance repositioning aircraft; as well as traffic to Runway 1L or 1R; to cross mid filed. So this was a night time; VMC; calm wind night coordination for crossing midfield between Local and Ground.The arrival was on about a five mile final when coordination took place to cross Runways 28L and 28R with this towing aircraft at Kilo. There was also a coordination to complete the crossing of Runway 28L at Delta with another aircraft under tow that was inconsequential to the event. The coordination was crossing on Grounds frequency after an aircraft landed Runway 28L. I told the arrival to turn left at Echo; traffic crossing downfield twice. They acknowledged and I advised Ground I had their acknowledgement and they issued the crossings. I believe they gave the Kilo crossing first; and then the Delta. In between; as soon as I had the exiting confirmed at Echo; I cleared an aircraft for takeoff Runway 1L; the arrival had just rolled through and was approaching Echo. This should have worked all day. As the aircraft under tow started moving at Kilo; they were looking good in my scan with their breakaway movement; then tragedy struck. I guess they were loaded with gas; because it did not work. Their extremely slow movement up to and over the hump (apex of the runway we normally see when an aircraft arrival has shut down one of their engines between the runways) and it takes just a little more for them to clear the middle high spot of the runway on crossing. It was decided at the beginning of the approach lights; it was not going to work.I sent the arrival aircraft around; with runway heading and three thousand; which they read back clearly and performed. I performed the coordination with NorCal Approach and then shipped them off to Departure. I would think that the tug driver would say out of caution that they were full of gas and heavier than usual before accepting the crossing; as this was very unusual for a regular crossing fleet with the Taxiway Zulu construction requiring midfield crossings.