So several points that I have mentioned to Mike and some additional concerns.
Based on the DOC he is using (0.3") with a 3/8" CCGT insert, as well as the size of the hole he is boring (1 9/16") he is actually pushing his current lathe and tooling beyond its physical limits. If you are stalling out the motor on the VFD, then you are exceeding the limitations of the machine in my opinion and something is going to break. An inverter/vector motor could help a bit but just means something else is eventually is going to fail. The main idea is to use a machine within it operating envelope.
The forward option is either to change how he is turning down stock, less DOC and increase the feed, as well as consideration of deep boring with a large carbide boring bar. I use a 1" and have bored up to 8" deep in steel, but the rate of removal is nowhere near hogging it out with a large MT drill.
So one reason why I felt that if one needs to upgrade for more aggressive turning, you would be better off with a larger heavier lathe, with a bigger spindle bore and a beefier tailstock that can take MT4 drills. This is based on direct experience with the 1340GT/ERL-1340/1440C and the larger RML/TL/TVS size lathes. Unfortunately there is a lot more cost to just upgrading the lathe as the latter machined benefit from CXA tool post holders which can achieve a 0.3" DOC.
Space wise it may be best to do a cardboard template/layout lines on the floor and work with whomever you are sharing the space with. If you need to get rid to the RPC, you can get an inexpensive $200) 1Hp Teco L510 VFD 120V with a voltage doubler and output 3 phase 240VAC. It is a no brainer install, connect the motor to the VFD terminals, connect the power in to a 120VAC plug, use either a single open/close switch for the run or two momentary switches (NC and NO) with 3 wire control in forward only direction. I will walk you through it if you need it. You have not worn me out yet, but getting there.
As far as the open Norton gearbox, they are messy. Many people weld up a trey to catch the oil that drips down or get some small disposable aluminum treys and mold it under the gearbox. If it is dripping oil down fromthe gearbox then you are most likely oiling it enough, my main issue with the stock single oiling port is you need way more oil pumped in to get to the other side. Other option is a pump oiler with a distribution system. This has been extensively posted on.