That is incorrect.
First I never said they check ID when purchasing. When you purchase a reloadable card it acts like a non-reloadable card UNTIL REGISTERED. You can't reload even a single dollar until registered. No exceptions. No reloadable card allows reloading of any amount (even a single dollar) would be a direct violation of FinCEN rules.
To reload requires registering the card. Anyone claiming anything different is mistaken or confused. The rules are (surprisingly for FinCEN) clear.non-reloadable - no ID required limited to max of $1,000 (although most brands limit it to $500)
reloadable - to reload required registration and verification of KYC/AML information HOWEVER the card can still act as a non-reloadable card until registered.
As an example here is green dot cardholder agreement:
https://www.greendot.com/greendot/cardholder-agreement-bank?issuingBank=GreenDotBankHow to Reload Your Card
You can add (reload) more money to your Card, once we have successfully verified
your personal information, at any Retailer or by following the directions supplied with the
Card.
Here is Walmart MoneyCard cardholder agreement
5. Using Your Temporary Card. Using Your Temporary Card.If you purchase and receive a Temporary Card in-store, you must load between $20 and $500 onto your Temporary Card (or up to $1,000 if the initial load is with a check cashed at Walmart).
...
You may not load additional funds on a Temporary Card until you activate your Card and we verify your identity.
...
6. Reloading Your Card. After we verify your identity, you may reload your Card at any Walmart store (except in VT and WY) or at any retailer participating in the network of reload locations operated by Green Dot. You also may arrange for direct deposit of your salary, wages or government benefits to your Card by completing and submitting to your employer or the appropriate government agency a form you can obtain by calling 1-877-937-4098 or by going online to walmartmoneycard.com.
Every other reloadable card has similar language.
For the OP use the Walmart card would be the best card if they allowed the $1,000 initial load to be paid by cash but they don't (>$500 requires a check). AFAIK all other reloadable cards limit the initial load to $500.