I've gotten myself stuck under the bar bench pressing, too. I bench in a gym and just beg people walking by to help me. It's embarrassing. I can't seem to figure out how to use the bench with the safety bars. I always end up hitting them every rep which freaks me out. I guess I'm not big enough to clear them. And the j-hooks on the bench with the safety bars are really unsafe making it harder to do the emergency rack into the lower hooks. Thing's a death trap. I'd rather endure the humiliation. Also, I've given up doing that last rep I'm not sure of.
You can buy a 12-gauge power rack (which can handle upwards of 600 lbs) for $245 on Amazon plus $99 shipping. And you can put your attempted ninth rep on the bench press @ 200 pounds right down on the pins (below your chest, but above your neck) when you have to, like I did tonight. Even with 2 guys spotting, we always set the pins (at the sixth hole for bench press, eighth for squats). Best $345 I ever spent.
Not being argumentative, but as a guy who started the program fat, you're better off starting to lift now and then getting lean later. Unless you can't physically do the lifts, there's no reason to not take advantage of the huge recovery capacity your body has at the moment. Yeah, you'll lose weight slower than you would if you did nothing but cardio, but you're getting stronger and building muscle so when you do some conditioning along with your lifting, you'll burn all the more calories.
Do you have a friend with a membership that can get you in for a free day or seven? I completely understand the difficult mental part of getting into the gym...we have issues with this at the Y all the time, where I train, and we consciously try to "buddy up" hesitant new members with board members or staff who use the Y to help get the ball rolling. Just a thought.
A pair of metal sawhorses will work as safeties too. Nothing like as good an option as a cage, but probably within your price range today. Put a bolt at each end through one of the holes usually pre-drilled in the tops of the sawhorses, to prevent a bar rolling off.
While your bench looks solidly built, I've always hated the 5-gallon-bucket approach to stands - the wobbling you see in your video shows why, even before someone gets to lifting ponderous weights. There's just not enough square footage on the bottom to be sure the things will stay upright if lightly bumped. If you must use home-built stands, please do something to address that instability, or there's gonna be a train wreck in your future. At a minimum, make a much bigger base, and do some very firmly attached diagonal bracing in all directions between the base and somewhere maybe 2 feet up the posts.
Frankly though? You'd be orders of magnitude better served in a gym. Doing the actual program, within a very short period of time you'd be lifting more than most of the people you're likely to see there, even if they "look" stronger. Being better than them will go a long ways towards addressing your understandable anxiety. And getting a regular lifting partner at the gym will be one of the most effective ways of keeping you consistently doing the program.
Best wishes,
t