Hi. Those ingredients are all fine (although I'm not keen on lentils in mixes), but making your own mix is not recommended without a lot of research and it can be quite complex calculating all the nutritional values. It is quite a difficult thing to achieve and getting the nutritional values right is very important so the hamster doesn't get some condition. Lack of protein can be one issue and can lead to fur loss or muscle problems but other nutritional needs are important too.
So I think it's better to just buy a good muesli mix, with the fortified vitamins and right balance of nutrition. If it's a bit low on protein, you can supplement that in a few ways.
You're correct that Higgins sunburst isn't the best option. Higgins Vita Garden is supposed to be better and is also sugar free. It's still not the best for variety but it contains everything needed, bar supplementing the protein which is only about 15% and they need 18 to 22% protein. It apparently contains probiotic as well which is a positive! I think Amazon in the US sell it.
www.higginspremium.com
I also agree that Oxbow isn't good to give - it has too much fibre and hay which prevents them absorbing other nutrients. It's more a food for guinea pigs than hamsters.
So for supplementing the protein you could either
a) supplement with fresh human food - a bit of chopped hard boiled egg or scrambled egg a couple of times a week, plus a nut a couple of times a week (Eg half a shelled walnut or pecan nut). Plain unsalted nuts or a monkey nut (peanuts in their shells). Or occasionally a bit of chicken if you have a roast chicken sometimes - any bit of cooked meat is fine if it's plain - no spices, sauces or gravies. But not processed meat. Teeny tiny bit no bigger than their ear.
b) use freeze dried shrimps or chicken pieces (finding the right freeze dried chicken can be difficult as some is raw freeze dried - some raw is ok if it's been pasteurised).
c) Add 2 or 3 pellets of science selective daily - this is an all in one pellet that contains everything needed including protein - if you can get it in the US. This is maybe the easier option if you can get it and just keep nuts, and fresh food as occasional additional treats!
Edit - looks like science selective isn't on amazon us any more!
Personally I do a) - they absolutely love a bit of egg! Any fresh human food they seem to love. They also love walnuts and pecan nuts and monkey nuts.
It's also good to give a piece of fresh veg every day. Every 3rd day at first if he's not used to it. But every day after a couple of weeks of that. Favourites seem to be cucumber and broccoli, or a pea. I find both cucumber and broccoli keep a while if kept in the fridge. But only a teeny tiny piece no bigger than their ear again. They eat it straight away then. Too much and they might hoard it and it go off.
It doesn't include hamster mixes, just all other foods. Hamster mixes we know about from experience.