Hi. I would still advise caution from my "Engineer's" head.... A bigger motor, or even down- gearing, is seemingly a good idea because you ultimately want more torque applied. This is to overcome the shearing force exerted by the tool on the metal at the appropriate speed and feed of cut. 2 solutions, as the lathe (bed and slides) can only manage a limited torque. (If you don't know, the cutting torque is related to how much metal you remove = width and depth of cut, diameter at point of cut, and shear-strength of material being cut, so your lathe may be OK with a 0.0005in cut at 1in diameter, but not OK at 2 in diameter, or 0.001in cut because those both need twice the torque applied. Similarly a 2 mm tool takesc2/3rd the torque of a 3mm tool at the same diameter, feed-rate and workpiece material. )
1: reduce the feed-rate, or increase speed of rotation so each revolution cuts less metal (reduced cut = reduced torque to within the capability of the lathe stiffness).
Or 2 : Reduce the width of cut - which is how a "Modified hacksaw" blade can work, when parting tools won't. Make a tool blade using a piece from a broken hacksaw blade - e.g. of un-used teeth just on the working side of the mounting hole. Select a tooth with a zero set as the cutting point. Make a precise holder so the blade is vertical. As the blade progresses into the cut the "kerf" from the set of the following blades will make the cut wider, but lubricate the cutting point as at the first tooth there is no side clearance - hence a lot of heat generated from the cutting shear, and side friction combined. I used this on a very small lathe, that had a big enough motor/gearing, but innadequate bed stiffness for cutting with my "regular" tool, on decent steel, at a larger diameter. But the feed was GENTLY, GENTLY! Not "stuff it in hard".
Sorry to be so long winded, but it is a complex problem, and £10,000 of lathe will have a much better (easier) capability than a £500 "hobby" lathe. I have a variable-speed cheap Chinese lathe and it is great! For what it cost. But at low speed it has hardly any torque, so like the spring loaded tool holder, it naturally stops the cut if I am too forceful for the stiffness of the whole machine. Not a problem as I have the time to work carefully within its limitations, and my local club has bigger industrial machines when needed.