For your biggerbolderbaking cream cheese recipe, you aren't making cream cheese, you're making paneer - whole milk that's curdled by lemon juice that makes a grainy cheese, which is often strains quite firm, and it doesn't melt or stretch well.
That blog is making something else, a soft cheese substitute that's just very soft unstrained and blended paneer. I suppose that can match texture if carefully curdled (I must imagine), and thoroughly blended with some water and whey to mechanically break up the curds, but it isn't cream cheese any more than scrambled tofu is scrambled eggs.
Cream cheese is made with cream (stretched with milk, often, but it does need the extra fat and the more cream, the better the flavor), and it's fermented much like yogurt is... you can often buy the cultures in the same place, and the procedure is much the same, and even sub them for the other in a pinch, though the flavors will be just a bit off. I've made it before, it's pretty fun and tasty.
In truth, most cheese is cultured - cheeses curdled with just lemon juice are rarer and mostly of the grainy firm curds variety like paneer. Cheeses often requires specific strains (the basics being mesophilic or thermophillic cultures for cheeses, and yogurt culture being the other major option), and often further curdled with rennet. You can find these ingredients online most anywhere.
If you're really interested in making a cream cheese substitute, with what's easily available, I'd suggest making yogurt cheese or greek yogurt - heat and cool the milk, culture with a spoonful of yogurt, then strain very well so the result is thick and creamy. You can find recipes all over the place with amounts, precise instructions, etc - and you can culture yogurt with storebought yogurt (with live cultures), so you don't need to be buying and shipping culture from all over the place. It would be creamy, thick, and fresh-tasting, if somewhat leaner that a true cream cheese... a decent substitute if you just want something approximate.
I am much less familiar with marscapone cheese, it looks like it's closer to thickened cream than curdled cheese. It looks some of the major factors are the fat content, the proportion of acid, and the handling.
Heavier cream apparently won't curdle like milk, since the proportion of fats to proteins is way off, so I'd guess the percentage would make a really big difference in this recipe. This may be aggravated by the acid content.
The other thing is, the proportion of acid needs to be quite low - one of your recipes calls for 2 1/2 tbs lemon for two and a half cups cream, the other for just 1 tbs per two cups, that's a really big difference. I'd guess lower fat content plus extra acid would make the cheese much grainier.
The third factor from what I can tell, is handling. One recipe mentions the cheese becoming grainy when using active, rather than passive straining, another mentions graininess when the cream is mixed too hard or too much. I'd guess it should be very gently or occasionally mixed once the lemon juice is introduced. It may help to add less acid but let it have more time to thicken so the process goes more gently.
You might be able to get a softer texture my mechanically breaking up the curds, mixing or blending, though there's no guarentee.
ps - you can't really "enrich" milk or cream with butter for higher fat content when it comes to recipes requiring cream, etc, they just doesn't combine on their own and emulsifiers are likely to mess with the curdling process. You can often make do with a lower fat content, it will just taste a bit differently, a bit less rich, but it's often tasty in its own right. You might, if you really want to try it, fold very soft butter into the cream cheese right when it's ready to store/serve/etc for a richer flavor... but I've no idea how it'd turn out and there may be other unexpected changes.