I get VOA in Shenzhen and from there on the away to Europe I have 3.5 hours layover in Beijing

Mike, after you have obtained Shenzhen VOA and entered mainland China, you can take a flight to a foreign country, but is has to be a nonstop direct flight. Unfortunately, in your case, you have a stop in Beijing and that disables you to use this option.

Another problem is in the fact that you cannot have two concurrent visas, so if you have a transit visa obtained in advance, you cannot apply for a Shenzhen VOA or vice versa.

The only solution in your case is to obtain a full Chinese visa (tourist - L type) in advance and to travel to Shenzhen and after that from Shenzhen to some other country with absolute peace of mind. Like this, you will not have to obtain a Shenzhen VOA and you will just take a high speed train from Hong Kong to Shenzhen or fly into Shenzhen from some other country and after your stay there, fly to the next country via Beijing.