Reading json file with large base64 values with C# - json.net

Question

I am using the NewtonSoft.Json package.
I need to parse a JSON file which contain large base64 encoded data chunks.
One base64 element could be 33 mb and the file will contain 30 of these.
The data could look like this (simplified):
{
"header": { "some_id": "foo", "other-data": 123},
"measurements": [
{
"info": {"unit": "m/s2","channel": "ch1"},
"data": "coUhRR.. 33 mb base64 data here ...=="
},
{
"info": { "unit": "m/s", "channel": "ch2"}
"data": "MxaDF.. 33 mb base64 data here ...=="
}, ...
]
}
I want to output the base64 bytes to separate files, preferably using the
CryptoStream and ToBase64Transform to transform the json value to bytes.
My problem is that the JsonTextReader keeps an internal char array, _chars.
This grows very large. Whenever a string value needs to be read, _chars doubles in size, starting at 1024 chars. Thus, if I am reading a 33 mb base64 element, _chars will grow to 64 million chars, taking up 128 mb of memory. And it doesn't shrink again for the lifetime of the JsonTextReader.
And in later versions, we will most likely need to handle even large json files.
How can I solve this issue? I assume I have to extend JsonTextReader in some way, but it is not obvious what to override?
An alternative would be to write a TextReader wrapper, which transformed the data above to a much shorter stream while routing the base64 data to files?
So it would do a simple on-the-fly parsing of the stream and transform
"data": "coUhRR.. 33 mb base64 data here ...=="
to
"data": "file:tempfile_xxx.bin"
while writing the decoded data to tempfile_xxx.bin. But then I need to use some clever black magic detect the right places to modify the stream?
Have I overlooked some obvious solution?
Is there an alternative parser, which would work better in this case?