Getting a TLB is a investment and satisifaction of job done yourself, not to save money on one project. After you are done, will you be able to use the BX for other things like mowing, maintaining property, diggin other holes for trees/shrubs etc? If you say yes to most of that, then go ahead and get the BX. To this day, I still kick myself on not owning a BX 10 years ago. All the money I spent on buying used and fixing the lawn tractors I couldve used it for the purchase of BX.
For the size of project you want to do, never having to do BH work before, I'd give you a week. You can certainly do it in a day or weekend, but don't run at 3000 rpms. It makes the BH "finicky" on the BX. Running at 2200 rpms will allow you to learn the controls and learn how the soil affects the bucket for efficent removal and do a straight/clean job. For a novice, it can be intimidation to use controls and just try to go up/down, left/right, curl/uncurl. Over time, when you get used to it, you can combine the movements and move up the RPMS for more power, faster job. Like I said, with lower RPMS, it allows you to understand the power of the curl to scoop instead of trying to power through the pull. Combining the two actions at high RPMS can look messy.
To sum it up- The BX is perfect job for what you need to do, but give yourself leeway in time. Too many factors can affect your timeline, soil conditions/types, rocks, roots, hidden obstacles. But on the other hand it can go smooth and be done in half a day. Good luck.