Advise and a hard won philosophy
I completely sympathize with your burning desire to create something very useful with nothing more than an inexpensive base and your enthusiasm. I suffer from that same form of insanity and have for over 70 years.
I once dreamed of making a banjo from a toilet seat and a Jonnie mop.
In my opinion, there is no way to even approach the worth and value of a tool and cutter grinder at used prices, by your expenditure of time and money in that futile quest.
Even a tired but decently equipped machine that needs some TLC and is priced accordingly, will get you much closer to the machine of your dreams, with far less effort and expense and it's designers had a much firmer grasp of useful functions and solutions for pitflls than you and I do.
I understand that your needs are modest, a handful of dull endmils but there's not much chance that you understand the needs that you'll have for sharpening tools, not long after you complete the Frankenmonster cheap lathe-cum-tool sharpener. And by complete, I mean give up on trying to make it do what it never could have done well.
It took me a long time to grasp that what I do to make a living, even a modest living, pays much more than time invested in futility. Haunt all sources of the machine tools you desire, like Craigslist, 'til that revivable jewel at give-away price turns up. Carry it home and marvel at the brilliance of it's design as your knowlege is increased by what it has to teach you.
An old, heavy antiquated plain bearing Galmeyer and Livingston T & C grinder was recently offered in my locale, for less than that HF junk costs. He finally unloaded it for $100. Vastly closer to the final goal you seek plus much more that you don't know to seek yet. As it stood, it could well accomplish your current needs and with some TLC, provide much more, that you don't even know that you need yet.
IMPORTANT: 3 more tips from my experience. Never let "heavy" sway your choice. Heavy only affects you once, (or until you need to move again) but crappy/light will effect you every time you flip on the switch and that effect will be disheartened/pissed! Heavy usually means better or best.
And further, a cheap little machine sitting on a rickety old dresser, takes up as much floor space as a real machine that does useful, precision work, EVERY TIME YOU USE IT! Avoid years of daily disappointment.
Finally, I missed out on so many truly great machines at little or even no expence, (free) that it makes me very sad. Why? Because of crippling ignorance about one thing, electricity. I'd whine, "that's worthless to me, it requires 3 phase power." Until I spent less than $200 and a weekend on the little project in the pic below, I could not capitalize on the
true bargains, industrial machines. Now I seek them out.
10 HP 3 phase rotary converter. Turns my household single phase power into industrial 3PH. True magic! A little more in the electrical cabinet out of sight above.
In my mid sixties, I hauled home 4,000 pounds of horizontal milling machine and accessories and moved it into it's resting place in my shop, by hand, with no danger or extreme effort. Just some thoughtful time and use of ordinary objects. Lot's of stories chronicling that sort of thing in detail on this forum.
My hope is that though there's little chance you'll give this much thought, that you'll remember it after several disappointments on the path you are now taking, the sooner, the better.
Bob