What did actually happen when Staudinger tried to synthesise diamond?
This is not really an answer, but more like a historical and literature review. Anyway, I hope it can help to further understand the reaction the the ideas behind.

First of all, thaditional Wurtz reaction suggests formation of 2D bonds such as $\ce{R^1 - R^2}$, whereas the idea in Staudinger's experiment is to obtain hree-dimensional network, ideally the the $\mathrm{sp^3}$ diamond hybrid state. Reaction of alkali metals with organics with high halogen content most likely will always lead to an explosion. For this reason qualitative Lassaigne's test should always be performed carefully, and one must not use fire extinguishers with tetrachloromethane for burning sodium.

According to the great review in [1, p. 8], the ﬁrst documented record of a combustion reaction between a metal and halocarbon compound refers to the ways of obtaining aluminium carbide for technical methane production. In 1907 Camille Matignon observed a very exothermic reaction between hexachlorobenzene and aluminium [2]:

$$\ce{10 Al + C6Cl6 -&gt;[\pu{225^\circ C}] 2 Al4C3 + 2 AlCl3}$$

In 1913 H. Staudinger published his attempts to synthesize ethylenedione $\ce{O=C=C=O}$ [3]. He suggested  abstracting the halogen atoms ($\ce{X}$) from either oxalyl chloride and -bromide $\ce{(COX)2}$ by a reaction with potassium or its sodium alloy ($\ce{NaK}$). This is one of the experiments performed by Staudinger (doing science was much more fun back then):


  In einer starken Bombe wurde aus 5 g Kalium und 5 g Natrium die flüssige Kalium-Natrium-Legierung hergestellt, dazu ein Röhrchen mit 8 g Oxalylbromid gegeben, und die Bombe nach dem vollständigen Evakuieren zugeschmolzen. Wenige Sekunden nach dem Zertrümmern des Röhrchens trat äußerst heftige Explosion unter gewaltiger Detonation ein, die nur durch glücklichen Zufall ohne erhebliche Beschädigung des einen von uns verlief.
  Liquid potassium-sodium alloy was prepared from 5 g of potassium and 5 g of sodium in a strong bomb, then a tube of 8 g of oxalyl bromide was added, and the bomb was melted after complete evacuation. A few seconds after the tube had been trimmed, and an extremely violent explosion ensued, with a great detonation, which proceeded only by chance without considerable damage to one of us.


Formation of an unknown highly reactive intermediate such as Dioxyacetylenkalium was suggested, but it was not confirmed experimentally.

A decade later, in 1922, Staudinger reported explosive reactions of alkali and alkaline earth metals with partially and perhalogenated solvents ($\ce{CH2Cl2}$, $\ce{CCl4}$). He again assumed the formation of different very instable species on contact that would be very sensitive to mechanical impact and thus trigger an explosive reaction. [4, part "5. Explosion mit Alkalimetallen"].

At the same time he also proposed usage of reaction between various alkali and alkaline earth metals ($\ce{Na, K, Ba}$) with halogenated organics with short $\ce{R}$ ("Rest des Moleküls") ($\ce{CH2Cl2}$, $\ce{CHCl3}$, $\ce{CCl4}$, $\ce{CH2Cl-CH2Cl}$, $\ce{CHCl2-CHCl2}$, $\ce{CHCl2-CCl3}$, $\ce{C2Cl6}$, $\ce{CHCl=CHCl}$, $\ce{CHCl=CCl2}$, $\ce{CCl2=CCl2}$, also corresponding $\ce{Br, I}$-derivatives) as an ammo detonating charges:


DE Patent 396,209 1922 "Verfahren zur Darstellung von Sprengmitteln" (DPMA Publikationsnummer CH 100 199 A);
DE Patent 391,346 1922 "Verfahren zur Initialzündung von Sprengstoffen" (DPMA Publikationsnummer CH 100 200 A).


He also underlined that the more halogenated the molecule is and the less other groups are present, the more vigorous the explosion will be. In addition, potassium shows better overall performance due to electropositivity ("Ver­gleicht man die Reaktionsfähigkeit der ver­
schiedenen Alkalimetalle, so ist das elektropositivste, das Kalium, das reaktionsfähigste, Lithium das reaktionsträgste"), but various amalgams or alkali metal mixtures will outperform potassium (flux).

Based on this, later its been proposed that the explosive reaction between sodium and tetrachloromethane to make diamond. His idea was implemented in late 1980s for obtaining diamonds in TNT/RDX detonation soot [5].

Finally, an autoclave synthesis based on original Staudinger work (funny enough, they didn't cite it) implementing sodium and tetrachloromethane [4] resulted in successful nanodiamond synthesis (in a 2% yield), and, subsequently, a well-recieved report in Nature in 1998 [6]:

$$\ce{CCl4 + 4Na -&gt;[\pu{700^\circ C, 48 h};  Ni-Co (cat)] C(diamond) + 4 NaCl}$$


  We call it the reduction-pyrolysis-catalysis (RPC) route. According to the free energy calculations $\Delta G^\circ (\text{diamond}) = \pu{-416.7 kcal mol^{-1}}$ and $\Delta G^\circ (\text{graphite}) = \pu{-417.4 kcal mol^{-1}}$,
  $$\ce{CCl4 + 4 Na -&gt; C(diamond) + 4 NaCl}$$
  and 
  $$\ce{CCl4 + 4 Na -&gt; C(graphite) + 4 NaCl}$$ 
  are thermodynamically spontaneous. Formation of graphite (amorphous carbon) and diamond is possible, and the yield of graphite (amorphous carbon) and diamond may be determined by kinetics.


The role of $\ce{Ni-Co}$ catalyst is not clear yet, and athors suggested than experimentation with other transition metals can potentially improve the process.

Review [1] points out that idea of diamond synthesing is mentioned in Staudinger's monography [7], though I failed to find this book, so unfortunately I cannot provide any substantial details from there.

Bibliography


Koch, E.-C. Metal-fluorocarbon based energetic materials; Wiley-VCH: Weinheim, 2012. ISBN 978-3-527-32920-5.
Matignon, C. Comptes rendus hebdomadaires des séances de l’Académie des sciences 1907, 145, 676–679.
Staudinger, H.; Anthes, E. Ber. Dtsch. Chem. Ges. 1913, 46 (2), 1426–1437. DOI 10.1002/cber.19130460222.
Staudinger, H. Angewandte Chemie 1922, 35 (93), 657–659. DOI 10.1002/ange.19220359302.
Greiner, N. R.; Phillips, D. S.; Johnson, J. D.; Volk, F. Nature 1988, 333 (6172), 440–442. DOI 10.1038/333440a0.
Li, Y.; Qian, Y.; Liao, H.; Ding, Y.; Yang, L.; Xu, C.; Li, F.; Zhou, G. Science 1998, 281 (5374), 246–247. DOI 10.1126/science.281.5374.246.
Staudinger, H. Arbeitserinnerungen; Hüthig Verlag, 1961.