Please correct me if I have misunderstood the situation.
You have misunderstood the situation.
As I understand it, transactions have to be recorded in a new block that is added to the blockchain.
To be considered "confirmed" and secure against doube-spending, yes the transactions have to be a part of the blockchain. The deeper they are in the blockchain the more difficult and expensive it is for someone to control enough hash power to modify the transaction.
Miners spend their time finding these blocks, and then they parcel the transactions in the new block.
Nope. First they choose the transactions and order them into a block of transactions. Then they generate a number, called a merkle root, that is dependent on the exact selection and ordering of the transactions. Then they build a header for the block. The header includes the merkle root, which is why they have to choose the transactions and order first. Then they repeatedly hash the header, incrementing a value called a "nonce" with each hash attempt until they either find a hash that is lower than the current target, or receive a valid block from a peer. Then they start the process all over again. If they find a hash that is lower than the current target, then they broadcast their block to all connected peers.
It's getting harder to find blocks,
Recently a lot of hash power has been added to the network. Therefore, the network has compensated by increasing the difficulty (by lowering the target hash value). The network adjusts the target every 2016 blocks in an attempt to keep the average rate of block solving around 10 minutes per block. If hash power is removed from the network, then the target will be increased which will make it easier to find blocks.
and the velocity of transfers is increasing.
I'm not sure what you mean by "velocity of transfers". Perhaps you're talking about "velocity of money"? If so, are you talking about the "transactions velocity of money" or the "income velocity of money"? I assume you must be talking about the transactions velocity of money, since you can currently get a reasonable estimate from the blockchain, whereas I'm not aware of any significantly trustworthy studies on the income velocity of money with bitcoin. It certainly seems that the transactions velocity has been generally increasing since the creation of bitcoin (with occasional temporary decreases).
Regardless of whether your're talking about income velocity or transaction velocity, how does this relate to the discussion in this thread?