Acknowledging those that have gone before with this one... I'd venture that there's a lot of Scots/Norse dialect at the root of the Newfoundland dialect, because the 'scurr' in scurrifunge is pretty clearly derived from the Old Norse 'skire' or 'skir', which had the meaning 'to cleanse, clear or purify'(c.1300) or 'clear of, free from, something morally bad' (c.1200)

Funge is interesting. According to the OED 'fung' is a common Scots variation of 'funk', which had the meaning (particularly of a horse) 'to strike or kick' and prance about kicking up dust (OED circa 1709). So a vigorous cleansing (with an element of chaotic energy and some disregard for gentleness) might be called a 'funging skirr' or 'skirring fung', hence (possibly) 'skirr-a-fung or scurrinfunge. Funk (as in 'blue funk') meaning cowardly or fearful probably comes from the same behaviours of a horse, but with the view that it's an undesirable trait, rather than an indication of vigour and alarming energy.

Acknowledging those that have gone before with this one... I'd venture that there's a lot of Scots/Norse dialect at the root of the Newfoundland dialect, because the 'scurr' in scurrifunge is pretty clearly derived from the Old Norse 'skire' or 'skir', which had the meaning 'to cleanse, clear or purify'(c.1300) or 'clear of, free from, something morally bad' As the Oxford English Dictionary has it:

skire ▪ I. skire, a.Obs.
Forms: 3, 5 skir, 5, 8–9 skire; 4–6, 9 skyre, 5 skyr.
[a. ON. sk{iacu}rr (Norw. and MSw. skir) clear, pure, = OE. sc{iacu}r shire a. In later use only Sc.]

1. Clear of, free from, something morally bad.
   c 1200 Ormin 8015 Þatt genge þatt wass milde & meoc,..& off galnesse skir & fre. Ibid. 12194 All þatt ahhte off eorþliȝ þing Þatt Godess þeowwess haffdenn..i þiss middell ærd Iss all skir fra þe deofell.
2. a. Of water: Pure, clear.
   13.. E.E. Allit. P. B. 1776 Þay..Asscaped ouer þe skyre watteres & scaþed þe walles. a 1400–50 Alexander 2119 Scamandra þe slire [read skire: Dubl. skyr] flode þe scriptour it callis.

Funge is interesting. According to the OED 'fung' is a common Scots variation of 'funk', which had the meaning (particularly of a horse) 'to strike or kick' and prance about kicking up dust. Again from the Oxford English Dictionary:

VII.funk, v.3Sc.north.
(fʌŋk)
[app. onomatopœic; a variant fung is common (see Jamieson).] trans. and intr. To kick.
c 1709 Auld Grey Mare i. in Jacobite Songs (1887) 56 You've curried the auld mare's hide, She'll funk nae mair at you. Ibid. v, The good auld yaud Could nowther funk nor fling. 1821 Blackw. Mag. Nov. X. 393 The horse funkit him aff into the dub. 1823 J. Wilson Trials Marg. Lyndsay xxxv. 294 The beast's funking like mad. 1834 M. Scott Cruise Midge (1859) 375 The quadruped funking up her heels and tossing the dry sand with her horns. 1892 Northumbld. Gloss., Funk, to kick, to kick up the heels as a horse or donkey does. ‘To funk off’ is to throw the rider.
Hence ˈfunking vbl. n. Also ˈfunker.
1823 Blackw. Mag. Mar. XIII. 313 It's hard to gar a wicked cout leave off funking. 1825–80 Jamieson s.v., Dinna buy that beast, she's a funker. 1852 R. S. Surtees Sponge's Sp. Tour (1893) 219 The move of the hounds caused a rush of gentlemen to their horses, and there was the usual scramblings up, and fidgetings, and funkings.

So a vigorous cleansing (with an element of chaotic energy and some disregard for gentleness) might be called a 'funging skirr' or 'skirring fung', hence (possibly) 'skirr-a-fung or scurrinfunge. Funk (as in 'blue funk') meaning cowardly or fearful probably comes from the same behaviours of a horse, but with the view that it's an undesirable trait, rather than an indication of vigour and alarming energy.