The difficulty in the primary sources when talking about money, is that often the 'payment' or 'transfer' of money between two nations was limited by the availability of coinage. Quite simply there was not enough physical coin to go around for all the needs as the right to mint coinage was tightly controlled by the ruling power. However, following almost a decade of wars across the British Isles by the time of the first transfer you mentioned, the available "cash" in the economy had grown, as both King, Parliament, Covenantors, and Confederates had been furiously minting their own coins, so too on a much smaller scale had their local garrisons and armies. Setting aside the propensity of civilians to bury their coins (many such coin hoards still being found today) when soldiers of any faction were nearby, the reality is there was much more hard currency in circulation per head of the population by 1647, than there was in, say 1637.
For the purposes of gathering such a vast sum of money together, to do so in not only hard currency, but in coins and plate of recognisable value to the recipient made it even more difficult. Such a sum would be understandably heavy and any form of transportation of that amount in any one movement would be far to risky a venture. As a result of the risks of transportation and the difficulties in accruing such an amount in cash, the amounts were broken down into smaller amounts, disbursed over a period of time. If we look to when the House of Lords discussed this £400,000 on the 13th January 1647 it was in the following terms 'Fifty Thousand Pounds, Part of the First Hundred Thousand Pounds of the last Two Hundred Thousand Pounds of the Four Hundred Thousand Pounds agreed to be paid to the Kingdom of Scotland'. So, the discussion is about a part of the total, and outlines how it had been broken down - in at least two parts (the last 200,000) which itself was further broken down into two halves (the first 100,000) and this in turn was broken down into the £50,000 under discussion. So the total amount was broken down into manageable, achievable amounts to be dispersed months apart 'That the aforesaid Fifty Thousand Pounds shall, at Twelve Months after the Payment of the Second Hundred Thousand Pounds of the said Four Hundred Thousand Pounds', so this £50,000 would have made up the paid total £250,000 of the £400,000 by that point.^(1)
Now, how this £50,000 was disbursed gives a clearer indication on how the whole £400,000 was managed - namely it was paid in specified amounts to certain people outlined by the Scots 'in Manner following ... 10,000l. to Archibald Marquis of Argyle, 1,333l 6s 8d to Dr John Sharpe, 3,866l 13s 4d to James Maxwell Esq. of Innerwick; 19,018l 12s 4d, to Sir W[illia]m Dick Knight; 6,069l, 15s, 4d to Mr. James Stewart, Bailiff of Edinburgh...' etc etc.^(2)
Now a 17th century wagon with a team of six horses could transport around two tons, so for the amount in cash for Argyll alone would only need a convoy of three wagons to move it, quite a small and achievable amount. However, the realities of paying individuals was much easier than paying a vague "state" - Argyll almost certainly took his payment not only in coin, but in credit and kind, so it is perhaps to say he would have been paid to the value of £10,000 pounds - a very large sum, but not unreasonable for one of the leading figures of in Scotland in terms of land, military power and the Scottish Covenanting government in the 1640s.
As to why individuals were selected for the disbursement of the monies, we come back to the overall lack of ready coinage and what would have been an extensive system of credit and debt settlement in its place - men such as Argyll would have been owed such money by the Scottish Covenanting government, having leant or spent those sums in its service - the Covenanter government was using this money to pay off its own debt owed to leading individuals.