It is by default not possible to combine Apache-2 licensed code with GPLv2-licensed code. Those licenses are incompatible. The Classpath Exception (CE) does provide a path towards compatibility, as long as the GPLv2+CE code and any other code are independent modules. According to the CE:
An independent module is a module which is not derived from or based on this library.
You copied some code from the JDK, this is fine under the GPLv2+CE. However, you should take care that this code is clearly separate from your other code (to satisfy the “independent module” requirement), and to properly comply with the GPLv2+CE license. It currently looks like your project might be in violation of the GPL.
So far, all the GPL-derived code is in a single class. But it does not appear as an independent module from the rest of your code. I would suggest you move that class to a separate top-level folder, and place it into a separate Java package.
To comply with the GPL, you will also have to include a copy of the GPL and state which changes you made to the code.
Finally, it is misleading to describe the resulting project as Apache-2 licensed, as it includes GPLv2+CE licensed code. This is not at all obvious from the current README or the LICENSE. Your license should accurately describe which parts of the code are available under which license.
Once you have licensed your source code properly, we can discuss licensing of binaries (i.e. pre-built JARs). Thanks to the classpath exception is is perfectly fine to publish these under the Apache license or any other license, without restrictions or attribution requirements. Therefore your project can be used in proprietary software.
Since properly complying with the GPLv2+CE takes some effort and complicates your project license, it may be much simpler to find another library that provides base64 encoding under a permissive license.
If your Base64 dialect only differs from a more standard Base64 encoding by the used character table, you could also just transliterate the base64-encoded data. E.g. if the default character table is AB...ab...89+/ and your table is .-AB...ab...89, you only have to map the data back to the encoding index and then look up the actual character in your table, no bit shifting required. So basically:
private static int getTableIndex(char c) {
if ('A' <= c && c <= 'A') return c - 'A';
if ('a' <= c && c <= 'z') return c - 'a' + 26;
if ('0' <= c && c <= '9') return c - '0' + 52;
if (c == '+') return 62;
if (c == '/') return 63;
throw some exception;
}
for (int i = 0 ... string.length)
string[i] = yourTable[getTableIndex(string[i])];
(For the avoidance of doubt, I wave any copyright or related rights for the above snippet to the fullest extend possible, using the CC0.)
