Welding the uprights to the wheel supports
Building a workshop gantry crane
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LudemannEngineering
Formula 1000 Race Car Blog
Welding the uprights to the wheel supports
Building a workshop gantry crane
LudemannEngineering 
Bracing from the upright member to the wheel carrier, (to just above the wheel mounts, like an upside down V) would greatly strengthen your crane. When travelling with a heavy load, raised up high, any sudden stop caused by an object in the path of a wheel say, would put a fair strain on the welds holding upright to wheel carrier. In addition, the load is presently applied to the centre of the wheel carrier, the best place if you wished to bend it, but the upside down V bracing would transfer it to above the wheels, greatly reducing the chance of the wheel carriers deforming under heavy loads.
I would also caution against using an angle grinder anywhere near your lathe, as grinding abrasive is given off in large amounts, and is very difficult to screen out. Any hot sparks are likely to melt plastic, and even using old woolen blankets which are heat resistant, but how do you remove them without spreading grinding residue, let alone use them again in the future without introducing the contaminants at that time. I would be looking to see why the carbide inserts were failing so frequently. Perhaps a different grade of carbide, or tool design, but if the main problem is lack of lathe rigidity, HSS may be a better option. Another option might be to remove from the chuck and part with the grinder well away from your machine tools. I should say that I have never done any grinding on the lathe, but fellow workers I have worked with in the past would first clean the lathe and remove all lubrication from the ways and all other external surfaces, including the chip pans and webbing on the bed. they would use degreaser or kero and clean the machine to within an inch of its life. The job would then be mounted and indicated in, and after that the machine would be covered with cloth and rag, and everything taped up. Even the chuck would be taped up if possible. Some would use a HD vacuum cleaner with funnel like end to capture as much dust as possible while the grinding was in progress, and they all used the vacuum cleaner and very fastidiously cleaned everything down once the job was done. The chuck was often stripped, cleaned and lubricated and the ways cleaned again with kero, and wiped down with paper toweling until no more muck came off. Once the machine was cleaned all over it would be re-lubricated, but not before the area immediately surrounding was vacuumed to rid the place of dust. They really worked hard to keep the grot out of their machines.
I offer the comments above as constructive criticism, make of them what you will, but I do congratulate you on your project, I wish to make a smaller version to run up and down inside a 40′ Hi Cube shipping container, and my present idea is for one like yours but with the modified “feet”. Thank you muchly for posting about yours.